{"id":801,"date":"2025-03-08T18:27:11","date_gmt":"2025-03-08T17:27:11","guid":{"rendered":"https:\/\/entangled-thoughts.com\/ar\/?p=801"},"modified":"2025-03-08T18:27:13","modified_gmt":"2025-03-08T17:27:13","slug":"%d9%85%d9%82%d8%af%d9%85%d8%a9-%d8%b9%d9%85%d9%84%d9%8a%d8%a9-%d9%84%d9%84%d9%85%d8%ad%d8%a7%d9%83%d8%a7%d8%a9-%d8%a7%d9%84%d8%ad%d8%a7%d8%b3%d9%88%d8%a8%d9%8a%d8%a9","status":"publish","type":"post","link":"https:\/\/entangled-thoughts.com\/ar\/%d9%85%d9%82%d8%af%d9%85%d8%a9-%d8%b9%d9%85%d9%84%d9%8a%d8%a9-%d9%84%d9%84%d9%85%d8%ad%d8%a7%d9%83%d8%a7%d8%a9-%d8%a7%d9%84%d8%ad%d8%a7%d8%b3%d9%88%d8%a8%d9%8a%d8%a9\/","title":{"rendered":"\u0645\u0642\u062f\u0645\u0629 \u0639\u0645\u0644\u064a\u0629 \u0644\u0644\u0645\u062d\u0627\u0643\u0627\u0629 \u0627\u0644\u062d\u0627\u0633\u0648\u0628\u064a\u0629: \u0641\u064a\u0632\u064a\u0627\u0621 \u0627\u0644\u0646\u0648\u0627\u0628\u0636"},"content":{"rendered":"\n<div style=\"border-radius: 10px; width: 100%; height: 500px;overflow: hidden;\"> <iframe loading=\"lazy\" src=\"https:\/\/entangled-thoughts.com\/ar\/demos\/mass-spring-damper\/\" width=\"100%\" height=\"100%\"><\/iframe> <\/div>\n\n\n\n<p><em><sup>\u062a\u0631\u0649 \u0641\u064a \u0627\u0644\u0625\u0637\u0627\u0631 \u0623\u0639\u0644\u0627\u0647 \u0645\u062d\u0627\u0643\u0627\u0629 \u062d\u0627\u0633\u0648\u0628\u064a\u0629 \u0644\u0641\u064a\u0632\u064a\u0627\u0621 \u0627\u0644\u0646\u0648\u0627\u0628\u0636 \u0648\u0647\u064a \u062a\u0639\u0645\u0644 \u0628\u0627\u0644\u0643\u0627\u0645\u0644 \u0641\u064a \u0645\u062a\u0635\u0641\u062d\u0643. \u064a\u0645\u0643\u0646\u0643 \u0627\u0644\u062a\u0641\u0627\u0639\u0644 \u0645\u0639\u0647\u0627 \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0627\u0644\u0645\u0627\u0648\u0633 \u0644\u062a\u063a\u064a\u064a\u0631 \u0645\u0646\u0638\u0648\u0631 \u0627\u0644\u0643\u0627\u0645\u064a\u0631\u0627 \u0623\u0648 \u062a\u0639\u062f\u064a\u0644 \u0645\u062f\u062e\u0644\u0627\u062a \u0627\u0644\u0645\u062d\u0627\u0643\u0627\u0629. \u064a\u0645\u0643\u0646\u0643 \u0643\u0630\u0644\u0643 \u0641\u062a\u062d \u0627\u0644\u0645\u062d\u0627\u0643\u0627\u0629 \u0641\u064a \u0635\u0641\u062d\u0629 \u062c\u062f\u064a\u062f\u0629 \u0628\u0627\u062a\u0628\u0627\u0639 \u0647\u0630\u0627 <a href=\"https:\/\/entangled-thoughts.com\/ar\/demos\/mass-spring-damper\/\" target=\"_blank\" rel=\"noreferrer noopener\">\u0627\u0644\u0631\u0627\u0628\u0637<\/a>. \u0627\u0644\u0643\u0648\u062f \u0627\u0644\u0645\u0635\u062f\u0631\u064a \u0643\u0627\u0645\u0644\u0627 \u0645\u0648\u062c\u0648\u062f <a href=\"https:\/\/github.com\/entangled-thoughts\/mass-spring-damper\" target=\"_blank\" rel=\"noreferrer noopener\">\u0647\u0646\u0627<\/a>.<\/sup><\/em><\/p>\n\n\n\n<p><a href=\"https:\/\/ar.wikipedia.org\/wiki\/%D9%85%D8%AD%D8%A7%D9%83%D8%A7%D8%A9_%D8%A8%D8%A7%D9%84%D8%AD%D8%A7%D8%B3%D9%88%D8%A8\">\u0627\u0644\u0645\u062d\u0627\u0643\u0627\u0629 \u0627\u0644\u062d\u0627\u0633\u0648\u0628\u064a\u0629<\/a> (<a href=\"https:\/\/en.wikipedia.org\/wiki\/Computer_simulation\">Computer Simulation<\/a>) \u0623\u062f\u0627\u0629 \u0642\u0648\u064a\u0629 \u062a\u064f\u0633\u062a\u062e\u062f\u0645 \u0641\u064a \u0645\u062e\u062a\u0644\u0641 \u0627\u0644\u062a\u062e\u0635\u0635\u0627\u062a \u0644\u0641\u0647\u0645 \u0633\u0644\u0648\u0643 \u0627\u0644\u0623\u0646\u0638\u0645\u0629 \u0627\u0644\u0645\u0639\u0642\u062f\u0629 \u0648\u0627\u0644\u062a\u0646\u0628\u0624 \u0628\u0647. \u0641\u0645\u0646 \u062e\u0644\u0627\u0644 \u0625\u0646\u0634\u0627\u0621 \u0646\u0645\u0627\u0630\u062c \u0631\u064a\u0627\u0636\u064a\u0629 \u0623\u0648 \u062d\u0633\u0627\u0628\u064a\u0629\u060c \u064a\u0645\u0643\u0646\u0646\u0627 \u0627\u0633\u062a\u0643\u0634\u0627\u0641 \u0633\u064a\u0646\u0627\u0631\u064a\u0648\u0647\u0627\u062a \u0635\u0639\u0628\u0629 \u0623\u0648 \u0645\u0643\u0644\u0641\u0629 \u0623\u0648 \u062d\u062a\u0649 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class=\"wp-block-heading\">\u0627\u0644\u0646\u0645\u0648\u0630\u062c \u0627\u0644\u0631\u064a\u0627\u0636\u064a<\/h2>\n\n\n\n<p>\u0627\u0644\u062e\u0637\u0648\u0629 \u0627\u0644\u062a\u0627\u0644\u064a\u0629 \u0641\u064a \u0628\u0646\u0627\u0621 \u0627\u0644\u0645\u062d\u0627\u0643\u0627\u0629 \u0647\u064a \u062a\u062d\u062f\u064a\u062f \u0627\u0644\u0646\u0645\u0648\u0630\u062c \u0627\u0644\u0631\u064a\u0627\u0636\u064a \u0627\u0644\u0630\u064a \u064a\u062d\u0643\u0645 \u062a\u0637\u0648\u0631 \u0627\u0644\u0646\u0638\u0627\u0645 \u0627\u0644\u062a\u064a \u062a\u0645 \u0645\u062d\u0627\u0643\u0627\u062a\u0647 \u0639\u0628\u0631 \u0627\u0644\u0632\u0645\u0646. \u0628\u0627\u0644\u0646\u0633\u0628\u0629 \u0644\u0644\u062c\u0633\u064a\u0645\u0627\u062a \u0627\u0644\u0646\u0642\u0637\u064a\u0629 \u064a\u0634\u0643\u0644 <a href=\"https:\/\/ar.wikipedia.org\/wiki\/%D9%82%D9%88%D8%A7%D9%86%D9%8A%D9%86_%D9%86%D9%8A%D9%88%D8%AA%D9%86_%D9%84%D9%84%D8%AD%D8%B1%D9%83%D8%A9\">\u0642\u0627\u0646\u0648\u0646 \u0646\u064a\u0648\u062a\u0646 \u0627\u0644\u062b\u0627\u0646\u064a<\/a> \u062d\u062c\u0631 \u0627\u0644\u0623\u0633\u0627\u0633 \u0627\u0644\u0630\u064a \u064a\u062d\u0643\u0645 \u0641\u064a\u0632\u064a\u0627\u0621 \u0647\u0630\u0647 \u0627\u0644\u062c\u0633\u064a\u0645\u0627\u062a \u0648\u064a\u0633\u0645\u062d \u0644\u0646\u0627 \u0628\u062d\u0633\u0627\u0628 \u062d\u0631\u0643\u062a\u0647\u0627 \u0645\u0646 \u062e\u0644\u0627\u0644 \u062a\u062d\u062f\u064a\u062f \u0627\u0644\u0642\u0648\u0649 \u0627\u0644\u0645\u0624\u062b\u0631\u0629 \u0628\u0647\u0627.<\/p>\n\n\n\n<p>\u064a\u062e\u0636\u0639 \u0627\u0644\u062c\u0633\u064a\u0645 \u0641\u064a \u0645\u062d\u0627\u0643\u0627\u062a\u0646\u0627 \u0644\u0642\u0648\u062a\u064a\u0646: \u0627\u0644\u0623\u0648\u0644\u0649 \u0647\u064a \u0627\u0644\u0642\u0648\u0629 \u0627\u0644\u0623\u0631\u062c\u0627\u0639\u064a\u0629 \u0644\u0644\u0646\u0627\u0628\u0636 \u0648\u0627\u0644\u062a\u064a \u062a\u062a\u0646\u0627\u0633\u0628 \u0637\u0631\u062f\u0627 \u0645\u0639 \u0627\u0644\u0627\u0633\u062a\u0637\u0627\u0644\u0629 \u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a \u062a\u062a\u0646\u0627\u0633\u0628 \u0637\u0631\u062f\u0627 \u0645\u0639 \u0645\u0648\u0636\u0639 \u0627\u0644\u062c\u0633\u064a\u0645 \\(x\\). \u0645\u0639\u0627\u0645\u0644 \u0627\u0644\u062a\u0646\u0627\u0633\u0628 \u0647\u0648 \u062b\u0627\u0628\u062a \u0627\u0644\u0635\u0644\u0627\u0628\u0629 \\(k\\) \u0648 \u062c\u0647\u0629 \u0627\u0644\u0642\u0648\u0629 \u0647\u064a \u0628\u062c\u0647\u0629 \u0645\u0639\u0627\u0643\u0633\u0629 \u0644\u0644\u0645\u0648\u0636\u0639 \u0644\u0623\u0646\u0647\u0627 \u062a\u0633\u0639\u0649 \u062f\u0627\u0626\u0645\u0627 \u0644\u0625\u0639\u0627\u062f\u0629 \u0627\u0644\u062c\u0633\u064a\u0645 \u0625\u0644\u0649 \u0645\u0648\u0636\u0639\u0647 \u0627\u0644\u0623\u0635\u0644\u064a. \u0627\u0644\u0642\u0648\u0629 \u0627\u0644\u062b\u0627\u0646\u064a\u0629 \u0647\u064a \u0627\u0644\u062a\u062e\u0645\u064a\u062f \u0648\u0627\u0644\u062a\u064a \u062a\u062a\u0646\u0627\u0633\u0628 \u0637\u0631\u062f\u0627 \u0645\u0639 \u0633\u0631\u0639\u0629 \u0627\u0644\u062c\u0633\u064a\u0645 \\(v\\) \u0628\u0645\u0639\u0627\u0645\u0644 \u062a\u0646\u0627\u0633\u0628 \u0647\u0648 \u062b\u0627\u0628\u062a \u0627\u0644\u062a\u062e\u0645\u064a\u062f. \u062c\u0647\u0629 \u0642\u0648\u0629 \u0627\u0644\u062a\u062e\u0645\u064a\u062f \u0645\u0639\u0627\u0643\u0633\u0629 \u0644\u062c\u0647\u0629 \u0627\u0644\u0633\u0631\u0639\u0629 \u0644\u0623\u0646\u0647\u0627 \u062a\u0633\u0639\u0649 \u0644\u0625\u0628\u0637\u0627\u0621 \u0627\u0644\u062c\u0633\u064a\u0645. \u0628\u0646\u0627\u0621\u0627\u064b \u0639\u0644\u0649 \u0630\u0644\u0643\u060c \u0641\u0625\u0646 \u0627\u0644\u0642\u0648\u0649 \u0627\u0644\u0645\u0624\u062b\u0631\u0629 \u0641\u064a \u0627\u0644\u062c\u0633\u064a\u0645 \\(F\\) \u0641\u064a \u0623\u064a \u0644\u062d\u0638\u0629 \u0632\u0645\u0646\u064a\u0629 \\(t\\) \u0647\u064a: $$ F(t) = -k\\ x(t)\\ &#8211; c\\ v(t) $$<\/p>\n\n\n\n<p>\u062d\u0633\u0628 \u0642\u0627\u0646\u0648\u0646 \u0646\u064a\u0648\u062a\u0646 \u0627\u0644\u062b\u0627\u0646\u064a \u0641\u0625\u0646 \u0647\u0630\u0647 \u0627\u0644\u0642\u0648\u0649 \u0627\u0644\u0645\u0624\u062b\u0631\u0629 \u0641\u064a \u0627\u0644\u062c\u0633\u064a\u0645 \u062a\u0633\u0628\u0628 \u062a\u0633\u0627\u0631\u0639\u0627\u064b \\(a\\) \u064a\u062a\u0646\u0627\u0633\u0628 \u0639\u0643\u0633\u0627 \u0645\u0639 \u0643\u062a\u0644\u062a\u0647: $$ a(t) = F(t)\/m $$<\/p>\n\n\n\n<p>\u064a\u0645\u062b\u0644 \u0627\u0644\u062a\u0633\u0627\u0631\u0639 \u0627\u0644\u062a\u063a\u064a\u0631 \u0627\u0644\u0622\u0646\u064a \u0641\u064a \u0633\u0631\u0639\u0629 \u0627\u0644\u062c\u0633\u064a\u0645 \\(v\\)\u060c \u0648\u064a\u064f\u0639\u0628\u0651\u0631 \u0639\u0646\u0647 \u0631\u064a\u0627\u0636\u064a\u0627 \u0643\u0645\u0634\u062a\u0642 \u0627\u0644\u0633\u0631\u0639\u0629 \u0628\u0627\u0644\u0646\u0633\u0628\u0629 \u0644\u0644\u0632\u0645\u0646: $$ a(t) = \\frac{dv}{dt}  $$ \u0643\u0630\u0644\u0643 \u062a\u0645\u062b\u0644 \u0627\u0644\u0633\u0631\u0639\u0629 \u0627\u0644\u062a\u063a\u064a\u0631 \u0627\u0644\u0622\u0646\u064a \u0641\u064a \u0645\u0648\u0636\u0639 \u0627\u0644\u062c\u0633\u0645 \\(x\\) \u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a \u0641\u0647\u064a \u0645\u0634\u062a\u0642 \u0627\u0644\u0645\u0648\u0636\u0639 \u0628\u0627\u0644\u0646\u0633\u0628\u0629 \u0644\u0644\u0632\u0645\u0646: $$ v(t) = \\frac{dx}{dt} $$<\/p>\n\n\n\n<p>\u062a\u0639\u0637\u064a \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0627\u0644\u0623\u0631\u0628\u0639\u0629 \u0623\u0639\u0644\u0627\u0647\u060c \u0628\u0627\u0644\u0625\u0636\u0627\u0641\u0629 \u0625\u0644\u0649 \u0627\u0644\u0645\u0648\u0636\u0639 \u0627\u0644\u0645\u0628\u062f\u0626\u064a \u0644\u0644\u062c\u0633\u064a\u0645 \\(x(0)=x_0\\) \u0648\u0633\u0631\u0639\u062a\u0647 \u0627\u0644\u0627\u0628\u062a\u062f\u0627\u0626\u064a\u0629 \\(v(0)=0\\)\u060c \u062a\u0648\u0635\u064a\u0641\u0627 \u0631\u064a\u0627\u0636\u064a\u0627 \u0643\u0627\u0645\u0644\u0627 \u0644\u062f\u064a\u0646\u0627\u0645\u064a\u0643\u064a\u0629 \u0627\u0644\u0646\u0638\u0627\u0645 \u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u0645\u062d\u0627\u0643\u0627\u0629. \u064a\u062f\u0639\u0649 \u0647\u0630\u0647 \u0627\u0644\u0646\u0648\u0639 \u0645\u0646 \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0628\u0640&#8221;<a href=\"https:\/\/ar.wikipedia.org\/wiki\/%D9%85%D8%B9%D8%A7%D8%AF%D9%84%D8%A9_%D8%AA%D9%81%D8%A7%D8%B6%D9%84%D9%8A%D8%A9\">\u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0627\u0644\u062a\u0641\u0627\u0636\u0644\u064a\u0629<\/a>&#8221; \u0646\u062a\u064a\u062c\u0629 \u0644\u0627\u062d\u062a\u0648\u0627\u0626\u0647\u0627 \u0639\u0644\u0649 \u0645\u0639\u0627\u0645\u0644 \u0627\u0644\u062a\u0641\u0627\u0636\u0644 (\u0627\u0644\u0645\u0634\u062a\u0642). \u0645\u0646 \u0623\u062c\u0644 \u062d\u0644 \u0647\u0630\u0647 \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0639\u0644\u0649 \u0627\u0644\u062d\u0627\u0633\u0648\u0628\u060c \u0641\u0625\u0646\u0646\u0627 \u0628\u062d\u0627\u062c\u0629 \u0625\u0644\u0649 \u0635\u064a\u063a\u0629 \u062a\u0642\u0631\u064a\u0628\u0629 \u062a\u0633\u0645\u062d \u0644\u0646\u0627 \u0628\u062a\u0645\u062b\u064a\u0644 \u0645\u0639\u0627\u0645\u0644 \u0627\u0644\u062a\u0641\u0627\u0636\u0644 \u062d\u0627\u0633\u0648\u0628\u064a\u0627 \u0648\u0644\u0648 \u0628\u0634\u0643\u0644 \u062a\u0642\u0631\u064a\u0628\u064a.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u0627\u0644\u062a\u0642\u0631\u064a\u0628 \u0627\u0644\u062d\u0633\u0627\u0628\u064a \u0644\u0644\u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0627\u0644\u062a\u0641\u0627\u0636\u0644\u064a\u0629<\/h2>\n\n\n\n<p>\u064a\u0645\u062b\u0644 \u0627\u0644\u0645\u0634\u062a\u0642 \u0641\u064a \u0644\u062d\u0638\u0629 \u0645\u0627 \u0627\u0644\u062a\u063a\u064a\u0631 \u0627\u0644\u0645\u062a\u0646\u0627\u0647\u064a \u0641\u064a \u0627\u0644\u0635\u063a\u0631 \u0641\u064a \u0642\u064a\u0645\u0629 \u0627\u0644\u062a\u0627\u0628\u0639 \u062e\u0644\u0627\u0644 \u0641\u062a\u0631\u0629 \u0632\u0645\u0646\u064a\u0629 \u0645\u062a\u0646\u0627\u0647\u064a\u0629 \u0641\u064a \u0627\u0644\u0635\u063a\u0631 \u062d\u0648\u0644 \u0647\u0630\u0647 \u0627\u0644\u0644\u062d\u0638\u0629. \u064a\u0645\u0643\u0646\u0646\u0627 \u062a\u0642\u0631\u064a\u0628 \u0647\u0630\u0647 \u0627\u0644\u0642\u064a\u0645\u0629 \u0628\u0627\u0644\u0641\u0631\u0642 \u0628\u064a\u0646 \u0642\u064a\u0645\u0629 \u0647\u0630\u0627 \u0627\u0644\u062a\u0627\u0628\u0639 \u0641\u064a \u0627\u0644\u0644\u062d\u0638\u0629 \u0627\u0644\u062d\u0627\u0644\u064a\u0629 \u0648\u0642\u064a\u0645\u062a\u0647 \u0641\u064a \u0644\u062d\u0638\u0629 \u0644\u0627\u062d\u0642\u0629 \u0642\u0631\u064a\u0628\u0629 \u0645\u0646\u0647\u0627: $$ \\frac{dx}{dt} \\approx \\frac{x(t+\\Delta t)\\ &#8211; x(t)}{\\Delta t} $$ \u0648\u062a\u0632\u062f\u0627\u062f \u062f\u0642\u0629 \u0647\u0630\u0627 \u0627\u0644\u062a\u0642\u0631\u064a\u0628 \u0643\u0644\u0645\u0627 \u0642\u0635\u0631\u062a \u0627\u0644\u0641\u062a\u0631\u0629 \u0627\u0644\u0632\u0645\u0646\u064a\u0629 \\(\\Delta t\\) \u0628\u064a\u0646 \u0627\u0644\u0644\u062d\u0638\u062a\u064a\u0646.<br>\u0628\u0634\u0643\u0644 \u0639\u0627\u0645\u060c \u062a\u062f\u0639\u0649 \u0647\u0630\u0647 \u0627\u0644\u0637\u0631\u064a\u0642\u0629 \u0641\u064a \u062a\u0642\u0631\u064a\u0628 \u0627\u0644\u0645\u0634\u062a\u0642 \u0628\u0640&#8221;<a href=\"https:\/\/ar.wikipedia.org\/wiki\/%D9%81%D8%B1%D9%82_%D9%85%D8%AD%D8%AF%D9%88%D8%AF\">\u0627\u0644\u0641\u0631\u0648\u0642 \u0627\u0644\u0645\u062d\u062f\u0648\u062f\u0629<\/a>&#8220;(<a href=\"https:\/\/en.wikipedia.org\/wiki\/Finite_difference\">Finite Diffrences<\/a>)\u060c \u0648\u0644\u0647\u0627 \u0623\u0646\u0648\u0627\u0639 \u0639\u062f\u064a\u062f\u0629 \u062a\u062e\u062a\u0644\u0641 \u062d\u0633\u0628 \u0639\u062f\u062f \u0642\u064a\u0645 \u0627\u0644\u062a\u0627\u0628\u0639 \u0627\u0644\u0645\u0633\u062a\u062e\u062f\u0645\u0629 \u0641\u064a \u0635\u064a\u063a\u0629 \u0627\u0644\u062a\u0642\u0631\u064a\u0628 \u0648 \u0627\u0644\u0644\u062d\u0638\u0627\u062a \u0627\u0644\u0632\u0645\u0646\u064a\u0629 \u0627\u0644\u062a\u064a \u062a\u0645 \u062a\u0642\u064a\u064a\u0645 \u0627\u0644\u062a\u0627\u0628\u0639 \u0639\u0646\u062f\u0647\u0627. \u0627\u0644\u0635\u064a\u063a\u0629 \u0627\u0644\u062a\u064a \u0627\u0633\u062a\u062e\u062f\u0645\u0646\u0647\u0627 \u0647\u0646\u0627\u060c \u0648\u062a\u062f\u0639\u0649 \u0628\u0640&#8221;\u0627\u0644\u0641\u0631\u0648\u0642 \u0627\u0644\u0623\u0645\u0627\u0645\u064a\u0629 \u0645\u0646 \u0627\u0644\u062f\u0631\u062c\u0629 \u0627\u0644\u0623\u0648\u0644\u0649&#8221; (First-oder Forward Difference)\u060c \u062a\u0639\u062a\u0628\u0631 \u0645\u0646 \u0623\u0628\u0633\u0637 \u0627\u0644\u0635\u064a\u063a \u062d\u064a\u062b \u062a\u062d\u062a\u0648\u064a \u0641\u0642\u0637 \u0642\u064a\u0645\u062a\u064a\u0646 \u0644\u0644\u062a\u0627\u0628\u0639 \u0625\u062d\u062f\u0627\u0647\u0627 \u0641\u064a \u0627\u0644\u0644\u062d\u0638\u0629 \u0627\u0644\u062d\u0627\u0644\u064a\u0629 \u0648\u0627\u0644\u0623\u062e\u0631\u0649 \u0641\u064a \u0644\u062d\u0638\u0629 \u0644\u0627\u062d\u0642\u0629.<\/p>\n\n\n\n<p>\u0633\u0646\u0642\u0648\u0645 \u0628\u0625\u0639\u0627\u062f\u0629 \u062a\u0631\u062a\u064a\u0628 \u0647\u0630\u0647 \u0627\u0644\u0635\u064a\u063a\u0629 \u0628\u0634\u0643\u0644 \u0623\u0643\u062b\u0631 \u0645\u0644\u0627\u0626\u0645\u0629 \u0644\u0627\u0633\u062a\u062e\u062f\u0627\u0645\u0647\u0627 \u0641\u064a \u062d\u0644 \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0627\u0644\u062a\u0641\u0627\u0636\u0644\u064a\u0629: $$ x(t+\\Delta t) \\approx x(t) + \\frac{dx}{dt} \u00a0 \\Delta t $$ \u064a\u062f\u0639\u0649 \u0647\u0630\u0627 \u0627\u0644\u0634\u0643\u0644 \u0628\u0640&#8221;\u0635\u064a\u063a\u0629 \u0623\u0648\u064a\u0644\u0631 \u0627\u0644\u0635\u0631\u064a\u062d\u0629 \u0645\u0646 \u0627\u0644\u062f\u0631\u062c\u0629 \u0627\u0644\u0623\u0648\u0644\u0649&#8221; (<a href=\"https:\/\/en.wikipedia.org\/wiki\/Euler_method\">First-order Explicit Euler Formula<\/a>) \u0648\u0647\u064a \u062a\u0639\u0628\u0631 \u0639\u0646 \u0642\u064a\u0645\u0629 \u0627\u0644\u062a\u0627\u0628\u0639 \u0641\u064a \u0627\u0644\u0644\u062d\u0638\u0629 \u0627\u0644\u062a\u0627\u0644\u064a\u0629 \u0628\u062f\u0644\u0627\u0644\u0629 \u0642\u064a\u0645\u062a\u0647 \u0641\u064a \u0627\u0644\u0644\u062d\u0638\u0629 \u0627\u0644\u062d\u0627\u0644\u064a\u0629 \u0648\u0642\u064a\u0645\u0629 \u0627\u0644\u0645\u0634\u062a\u0642.<\/p>\n\n\n\n<p>\u0628\u0645\u0633\u0627\u0639\u062f\u0629 \u0647\u0630\u0647 \u0627\u0644\u0635\u064a\u063a\u0629 \u064a\u0645\u0643\u0646\u0646\u0627 \u0627\u0644\u0623\u0646 \u0643\u062a\u0627\u0628\u0629 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0627\u0644\u0646\u0645\u0648\u0630\u062c \u0627\u0644\u0631\u064a\u0627\u0636\u064a \u0628\u0627\u0644\u0634\u0643\u0644 \u0627\u0644\u062a\u0627\u0644\u064a \u0627\u0644\u0645\u0646\u0627\u0633\u0628 \u0644\u0644\u0645\u062d\u0627\u0643\u0627\u0629 \u0627\u0644\u062d\u0627\u0633\u0648\u0628\u064a\u0629:<br>$$ \\begin{align} F(t) &amp;= -k\\ x(t)\\ &#8211; c\\ v(t) \\tag{Eq. 1}\\\\&nbsp; a(t) &amp;= F(t)\/m \\tag{Eq. 2} \\\\ v(t+\\Delta t) &amp;\\approx v(t) + a(t)&nbsp; \\Delta t \\tag{Eq. 3}&nbsp; \\\\&nbsp; x(t+\\Delta t) &amp;\\approx x(t) + v(t)&nbsp; \\Delta t \\tag{Eq. 4}&nbsp; \\end{align}$$ \u064a\u0633\u0645\u062d \u0647\u0630\u0627 \u0627\u0644\u0634\u0643\u0644 \u0628\u062d\u0633\u0627\u0628 \u062a\u0642\u0631\u064a\u0628\u064a \u0644\u0645\u0648\u0636\u0639 \u0627\u0644\u062c\u0633\u064a\u0645 \u0648\u0633\u0631\u0639\u062a\u0647 \u0641\u064a \u0644\u062d\u0638\u0629 \u0632\u0645\u0646\u064a\u0629 \u0644\u0627\u062d\u0642\u0629 \u0628\u062f\u0644\u0627\u0644\u0629 \u0642\u064a\u0645\u062a\u0647\u0645 \u0641\u064a \u0644\u062d\u0638\u0629 \u0632\u0645\u0646\u064a\u0629 \u0633\u0627\u0628\u0642\u0629 \u0642\u0631\u064a\u0628\u0629 \u0645\u0646\u0647\u0627. <\/p>\n\n\n\n<p> \u064a\u0632\u062f\u0627\u062f \u062e\u0637\u0623 \u0627\u0644\u062a\u0642\u0631\u064a\u0628 \u0641\u064a \u062d\u0633\u0627\u0628 \u0627\u0644\u0645\u0648\u0636\u0639 \u0648\u0627\u0644\u0633\u0631\u0639\u0629 \u0641\u064a \u0627\u0644\u0644\u062d\u0638\u0629 \u0627\u0644\u062c\u062f\u064a\u062f\u0629 \u0643\u0644\u0645\u0627 \u0627\u0632\u062f\u0627\u062a \u0627\u0644\u0641\u062a\u0631\u0629 \u0627\u0644\u0632\u0645\u0646\u064a\u0629 \u0627\u0644\u0641\u0627\u0635\u0644\u0629 \u0628\u064a\u0646 \u0627\u0644\u0644\u062d\u0638\u062a\u064a\u0646 \\(\\Delta t\\). \u0648\u0644\u0643\u0646 \u0645\u0627\u0630\u0627 \u0644\u0648 \u0623\u0631\u062f\u0646\u0627 \u0645\u062d\u0627\u0643\u0627\u0629 \u0627\u0644\u0646\u0638\u0627\u0645 \u0644\u0641\u062a\u0631\u0629 \u0632\u0645\u0646\u064a\u0629 \u0637\u0648\u064a\u0644\u0629\u061f \u0639\u0646\u062f\u0647\u0627 \u0641\u0625\u0646\u0646\u0627 \u0628\u062d\u0627\u062c\u0629 \u0644\u062a\u0642\u0633\u064a\u0645 \u0647\u0630\u0647 \u0627\u0644\u0641\u062a\u0631\u0629 \u0627\u0644\u0637\u0648\u064a\u0644\u0629 \u0625\u0644\u0649 \u062e\u0637\u0648\u0627\u062a \u0632\u0645\u0646\u064a\u0629 \u0642\u0635\u064a\u0631\u0629 \u062c\u062f\u0627 \u0648\u062a\u0637\u0628\u064a\u0642 \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0628\u0634\u0643\u0644 \u0645\u062a\u0643\u0631\u0631. \u062a\u0639\u062a\u0645\u062f \u062f\u0642\u0629 \u0627\u0644\u0645\u062d\u0627\u0643\u0627\u0629 \u0639\u0644\u0649 \u0637\u0648\u0644 \u0627\u0644\u062e\u0637\u0648\u0629 \u0627\u0644\u0632\u0645\u0646\u064a\u0629 \u0627\u0644\u0642\u0635\u064a\u0631\u0629\u060c \u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a \u0641\u0625\u0646 \u0632\u064a\u0627\u062f\u0629 \u062f\u0642\u0629 \u0627\u0644\u0645\u062d\u0627\u0643\u0627\u0629 \u062a\u062a\u0637\u0644\u0628 \u0639\u062f\u062f \u0623\u0643\u0628\u0631 \u0645\u0646 \u0627\u0644\u062e\u0637\u0648\u0627\u062a \u0627\u0644\u062d\u0633\u0627\u0628\u064a\u0629.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u0627\u0644\u0643\u0648\u062f \u0627\u0644\u0628\u0631\u0645\u062c\u064a \u0644\u0644\u0645\u062d\u0627\u0643\u0627\u0629 \u0627\u0644\u0641\u064a\u0632\u064a\u0627\u0626\u064a\u0629<\/h2>\n\n\n\n<p>\u0641\u064a\u0645\u0627 \u064a\u0644\u064a \u0643\u0648\u062f \u0628\u0631\u0645\u062c\u064a \u0645\u0628\u0633\u0637 \u0644\u0645\u062d\u0627\u0643\u0627\u0629 \u0646\u0638\u0627\u0645 \u0627\u0644\u0643\u062a\u0644\u0629-\u0646\u0627\u0628\u0636 -\u0645\u062e\u0645\u062f \u0648\u0641\u0642 \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0627\u0644\u0633\u0627\u0628\u0642\u0629 \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0644\u063a\u0629 JavaScript:<\/p>\n\n\n\n<div class=\"wp-block-kevinbatdorf-code-block-pro cbp-has-line-numbers\" data-code-block-pro-font-family=\"Code-Pro-JetBrains-Mono\" style=\"font-size:.875rem;font-family:Code-Pro-JetBrains-Mono,ui-monospace,SFMono-Regular,Menlo,Monaco,Consolas,monospace;--cbp-line-number-color:#D4D4D4;--cbp-line-number-width:calc(2 * 0.6 * .875rem);line-height:1.25rem;--cbp-tab-width:2;tab-size:var(--cbp-tab-width, 2)\"><span role=\"button\" tabindex=\"0\" data-code=\"class MassSpringDamperPhysics {\n    constructor(mass, stifness, dampness, displacement) {\n        this.mass = mass; \n        this.stifness = stifness; \n        this.dampness = dampness;\n        this.position = displacement;\n        this.velocity = 0;\n    }\n\n    advance(elapsedTime) {\n        const maxTimeStep = 0.01;\n        let timeStep;\n\n        while (elapsedTime &gt; 0) {\n            if (elapsedTime &gt; maxTimeStep) {\n                timeStep = maxTimeStep;\n                elapsedTime -= maxTimeStep;\n            } else {\n                timeStep = elapsedTime;\n                elapsedTime = 0;\n            }\n            \n            var force = -this.stifness * this.position - this.dampness * this.velocity; \/\/Eq. 1\n            var acceleration = force \/ this.mass; \/\/Eq. 2\n            this.velocity += acceleration * timeStep; \/\/Eq. 3\n            this.position += this.velocity * timeStep; \/\/Eq. 4\n        }\n    }\n}\" style=\"color:#D4D4D4;display:none\" aria-label=\"Copy\" class=\"code-block-pro-copy-button\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" style=\"width:24px;height:24px\" fill=\"none\" viewBox=\"0 0 24 24\" stroke=\"currentColor\" stroke-width=\"2\"><path class=\"with-check\" stroke-linecap=\"round\" stroke-linejoin=\"round\" d=\"M9 5H7a2 2 0 00-2 2v12a2 2 0 002 2h10a2 2 0 002-2V7a2 2 0 00-2-2h-2M9 5a2 2 0 002 2h2a2 2 0 002-2M9 5a2 2 0 012-2h2a2 2 0 012 2m-6 9l2 2 4-4\"><\/path><path class=\"without-check\" stroke-linecap=\"round\" stroke-linejoin=\"round\" d=\"M9 5H7a2 2 0 00-2 2v12a2 2 0 002 2h10a2 2 0 002-2V7a2 2 0 00-2-2h-2M9 5a2 2 0 002 2h2a2 2 0 002-2M9 5a2 2 0 012-2h2a2 2 0 012 2\"><\/path><\/svg><\/span><pre class=\"shiki dark-plus\" style=\"background-color: #1E1E1E\" tabindex=\"0\"><code><span class=\"line\"><span style=\"color: #569CD6\">class<\/span><span style=\"color: #D4D4D4\"> <\/span><span style=\"color: #4EC9B0\">MassSpringDamperPhysics<\/span><span style=\"color: #D4D4D4\"> {<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">    <\/span><span style=\"color: #569CD6\">constructor<\/span><span style=\"color: #D4D4D4\">(<\/span><span style=\"color: #9CDCFE\">mass<\/span><span style=\"color: #D4D4D4\">, <\/span><span style=\"color: #9CDCFE\">stifness<\/span><span style=\"color: #D4D4D4\">, <\/span><span style=\"color: #9CDCFE\">dampness<\/span><span style=\"color: #D4D4D4\">, <\/span><span style=\"color: #9CDCFE\">displacement<\/span><span style=\"color: #D4D4D4\">) {<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">        <\/span><span style=\"color: #569CD6\">this<\/span><span style=\"color: #D4D4D4\">.<\/span><span style=\"color: #9CDCFE\">mass<\/span><span style=\"color: #D4D4D4\"> = <\/span><span style=\"color: #9CDCFE\">mass<\/span><span style=\"color: #D4D4D4\">; <\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">        <\/span><span style=\"color: #569CD6\">this<\/span><span style=\"color: #D4D4D4\">.<\/span><span style=\"color: #9CDCFE\">stifness<\/span><span style=\"color: #D4D4D4\"> = <\/span><span style=\"color: #9CDCFE\">stifness<\/span><span style=\"color: #D4D4D4\">; <\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">        <\/span><span style=\"color: #569CD6\">this<\/span><span style=\"color: #D4D4D4\">.<\/span><span style=\"color: #9CDCFE\">dampness<\/span><span style=\"color: #D4D4D4\"> = <\/span><span style=\"color: #9CDCFE\">dampness<\/span><span style=\"color: #D4D4D4\">;<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">        <\/span><span style=\"color: #569CD6\">this<\/span><span style=\"color: #D4D4D4\">.<\/span><span style=\"color: #9CDCFE\">position<\/span><span style=\"color: #D4D4D4\"> = <\/span><span style=\"color: #9CDCFE\">displacement<\/span><span style=\"color: #D4D4D4\">;<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">        <\/span><span style=\"color: #569CD6\">this<\/span><span style=\"color: #D4D4D4\">.<\/span><span style=\"color: #9CDCFE\">velocity<\/span><span style=\"color: #D4D4D4\"> = <\/span><span style=\"color: #B5CEA8\">0<\/span><span style=\"color: #D4D4D4\">;<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">    }<\/span><\/span>\n<span class=\"line\"><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">    <\/span><span style=\"color: #DCDCAA\">advance<\/span><span style=\"color: #D4D4D4\">(<\/span><span style=\"color: #9CDCFE\">elapsedTime<\/span><span style=\"color: #D4D4D4\">) {<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">        <\/span><span style=\"color: #569CD6\">const<\/span><span style=\"color: #D4D4D4\"> <\/span><span style=\"color: #4FC1FF\">maxTimeStep<\/span><span style=\"color: #D4D4D4\"> = <\/span><span style=\"color: #B5CEA8\">0.01<\/span><span style=\"color: #D4D4D4\">;<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">        <\/span><span style=\"color: #569CD6\">let<\/span><span style=\"color: #D4D4D4\"> <\/span><span style=\"color: #9CDCFE\">timeStep<\/span><span style=\"color: #D4D4D4\">;<\/span><\/span>\n<span class=\"line\"><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">        <\/span><span style=\"color: #C586C0\">while<\/span><span style=\"color: #D4D4D4\"> (<\/span><span style=\"color: #9CDCFE\">elapsedTime<\/span><span style=\"color: #D4D4D4\"> &gt; <\/span><span style=\"color: #B5CEA8\">0<\/span><span style=\"color: #D4D4D4\">) {<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">            <\/span><span style=\"color: #C586C0\">if<\/span><span style=\"color: #D4D4D4\"> (<\/span><span style=\"color: #9CDCFE\">elapsedTime<\/span><span style=\"color: #D4D4D4\"> &gt; <\/span><span style=\"color: #9CDCFE\">maxTimeStep<\/span><span style=\"color: #D4D4D4\">) {<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">                <\/span><span style=\"color: #9CDCFE\">timeStep<\/span><span style=\"color: #D4D4D4\"> = <\/span><span style=\"color: #9CDCFE\">maxTimeStep<\/span><span style=\"color: #D4D4D4\">;<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">                <\/span><span style=\"color: #9CDCFE\">elapsedTime<\/span><span style=\"color: #D4D4D4\"> -= <\/span><span style=\"color: #9CDCFE\">maxTimeStep<\/span><span style=\"color: #D4D4D4\">;<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">            } <\/span><span style=\"color: #C586C0\">else<\/span><span style=\"color: #D4D4D4\"> {<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">                <\/span><span style=\"color: #9CDCFE\">timeStep<\/span><span style=\"color: #D4D4D4\"> = <\/span><span style=\"color: #9CDCFE\">elapsedTime<\/span><span style=\"color: #D4D4D4\">;<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">                <\/span><span style=\"color: #9CDCFE\">elapsedTime<\/span><span style=\"color: #D4D4D4\"> = <\/span><span style=\"color: #B5CEA8\">0<\/span><span style=\"color: #D4D4D4\">;<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">            }<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">            <\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">            <\/span><span style=\"color: #569CD6\">var<\/span><span style=\"color: #D4D4D4\"> <\/span><span style=\"color: #9CDCFE\">force<\/span><span style=\"color: #D4D4D4\"> = -<\/span><span style=\"color: #569CD6\">this<\/span><span style=\"color: #D4D4D4\">.<\/span><span style=\"color: #9CDCFE\">stifness<\/span><span style=\"color: #D4D4D4\"> * <\/span><span style=\"color: #569CD6\">this<\/span><span style=\"color: #D4D4D4\">.<\/span><span style=\"color: #9CDCFE\">position<\/span><span style=\"color: #D4D4D4\"> - <\/span><span style=\"color: #569CD6\">this<\/span><span style=\"color: #D4D4D4\">.<\/span><span style=\"color: #9CDCFE\">dampness<\/span><span style=\"color: #D4D4D4\"> * <\/span><span style=\"color: #569CD6\">this<\/span><span style=\"color: #D4D4D4\">.<\/span><span style=\"color: #9CDCFE\">velocity<\/span><span style=\"color: #D4D4D4\">; <\/span><span style=\"color: #6A9955\">\/\/Eq. 1<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">            <\/span><span style=\"color: #569CD6\">var<\/span><span style=\"color: #D4D4D4\"> <\/span><span style=\"color: #9CDCFE\">acceleration<\/span><span style=\"color: #D4D4D4\"> = <\/span><span style=\"color: #9CDCFE\">force<\/span><span style=\"color: #D4D4D4\"> \/ <\/span><span style=\"color: #569CD6\">this<\/span><span style=\"color: #D4D4D4\">.<\/span><span style=\"color: #9CDCFE\">mass<\/span><span style=\"color: #D4D4D4\">; <\/span><span style=\"color: #6A9955\">\/\/Eq. 2<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">            <\/span><span style=\"color: #569CD6\">this<\/span><span style=\"color: #D4D4D4\">.<\/span><span style=\"color: #9CDCFE\">velocity<\/span><span style=\"color: #D4D4D4\"> += <\/span><span style=\"color: #9CDCFE\">acceleration<\/span><span style=\"color: #D4D4D4\"> * <\/span><span style=\"color: #9CDCFE\">timeStep<\/span><span style=\"color: #D4D4D4\">; <\/span><span style=\"color: #6A9955\">\/\/Eq. 3<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">            <\/span><span style=\"color: #569CD6\">this<\/span><span style=\"color: #D4D4D4\">.<\/span><span style=\"color: #9CDCFE\">position<\/span><span style=\"color: #D4D4D4\"> += <\/span><span style=\"color: #569CD6\">this<\/span><span style=\"color: #D4D4D4\">.<\/span><span style=\"color: #9CDCFE\">velocity<\/span><span style=\"color: #D4D4D4\"> * <\/span><span style=\"color: #9CDCFE\">timeStep<\/span><span style=\"color: #D4D4D4\">; <\/span><span style=\"color: #6A9955\">\/\/Eq. 4<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">        }<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">    }<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">}<\/span><\/span><\/code><\/pre><\/div>\n\n\n\n<p><\/p>\n\n\n\n<p>\u0644\u062f\u064a\u0646\u0627 \u0647\u0646\u0627 \u0635\u0641 \u0628\u0631\u0645\u062c\u064a (class) \u064a\u0645\u062b\u0644 \u062d\u0627\u0644\u0629 \u0627\u0644\u0646\u0638\u0627\u0645 \u0641\u064a \u0623\u064a \u0644\u062d\u0638\u0629. \u0646\u062e\u0632\u0646 \u0641\u064a \u0627\u0644\u0645\u062a\u062d\u0648\u0644\u0627\u062a: <code>mass, stifness, dampness<\/code> \u0645\u062f\u062e\u0644\u0627\u062a \u0627\u0644\u0645\u062d\u0627\u0643\u0627\u0629: \u0627\u0644\u0643\u062a\u0644\u0629 \\(m\\)\u060c \u0627\u0644\u0635\u0644\u0627\u0628\u0629 \\(k\\)\u060c \u0627\u0644\u062a\u062e\u0645\u064a\u062f \\(c\\). \u0628\u064a\u0646\u0645\u0627 \u0646\u062e\u0632\u0646 \u0641\u064a \u0627\u0644\u0645\u062a\u062d\u0648\u0644\u0627\u062a <code>position, velocity<\/code> \u0645\u0648\u0636\u0639 \u0627\u0644\u062c\u0633\u064a\u0645 \\(x\\) \u0627\u0644\u062d\u0627\u0644\u064a \u0648\u0633\u0631\u0639\u062a\u0647 \\(v\\) \u0648\u0646\u0642\u0648\u0645 \u0628\u062a\u0647\u064a\u0626\u062a\u0647\u0627 \u0648\u0641\u0642 \u0627\u0644\u0634\u0631\u0648\u0637 \u0627\u0644\u0627\u0628\u062a\u062f\u0627\u0626\u064a\u0629\u060c \u0623\u064a \u062a\u0647\u064a\u0626\u0629 \u0627\u0644\u0645\u0648\u0636\u0639 \u0628\u0645\u062f\u062e\u0644 \u0627\u0644\u0645\u062d\u0627\u0643\u0627\u0629 <code>displacment<\/code> \u0648\u0627\u0644\u0630\u064a \u064a\u0645\u062b\u0644 \u0627\u0644\u0627\u0646\u0632\u064a\u0627\u062d \u0627\u0644\u0645\u0628\u062f\u0626\u064a \\(x_0\\)\u060c \u0648\u062a\u0647\u064a\u0626\u0629 \u0627\u0644\u0633\u0631\u0639\u0629 \u0628\u0627\u0644\u0642\u064a\u0645\u0629 \u0635\u0641\u0631. \u0644\u0627\u062d\u0638 \u0623\u0646\u0646\u0627 \u0644\u0645 \u0646\u0642\u0645 \u0628\u062a\u062e\u0632\u064a\u0646 \u0627\u0644\u062a\u0633\u0627\u0631\u0639 \u0648\u0627\u0644\u0642\u0648\u0649 \u0628\u0634\u0643\u0644 \u062f\u0627\u0626\u0645 \u0644\u0623\u0646\u0646\u0627 \u064a\u0645\u0643\u0646\u0646\u0627 \u062f\u0627\u0626\u0645\u0627 \u062d\u0633\u0627\u0628\u0647\u0645 \u0645\u0646 \u0627\u0644\u0645\u0648\u0636\u0639 \u0648\u0627\u0644\u0633\u0631\u0639\u0629 \u0648\u0641\u0642 \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u062a\u064a\u0646 (Eq. 1-2).<br><br>\u064a\u0645\u062a\u0644\u0643 \u0647\u0630\u0627 \u0627\u0644\u0635\u0641 \u0627\u0644\u0628\u0631\u0645\u062c\u064a \u062a\u0627\u0628\u0639 <code>advance<\/code> \u064a\u0642\u0648\u0645 \u0628\u062a\u062d\u062f\u064a\u062b \u0645\u0648\u0636\u0639 \u0648\u0633\u0631\u0639\u0629 \u0627\u0644\u062c\u0633\u064a\u0645 \u0628\u0639\u062f \u0645\u0631\u0648\u0631 \u0641\u062a\u0631\u0629 \u0632\u0645\u0646\u064a\u0629 <code>elapsedTime<\/code>. \u0643\u0645\u0627 \u0630\u0643\u0631\u0646\u0627 \u0633\u0627\u0628\u0642\u0627 \u0641\u0625\u0646\u0646\u0627 \u0644\u0627\u0646\u0633\u062a\u0637\u064a\u0639 \u062a\u0637\u0628\u064a\u0642 \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u062a\u064a\u0646 (Eq. 3-4) \u0625\u0644\u0627 \u0627\u0630\u0627 \u0643\u0627\u0646\u062a \u062a\u0644\u0643 \u0627\u0644\u0641\u062a\u0631\u0629 \u0627\u0644\u0632\u0645\u0646\u064a\u0629 \u0642\u0635\u064a\u0631\u0629 \u062c\u062f\u0627\u060c \u0644\u0630\u0644\u0643 \u0641\u0625\u0646\u0646\u0627 \u0646\u0633\u062a\u062e\u062f\u0645 \u062d\u062f \u0623\u0639\u0644\u0649 \u0644\u0644\u062e\u0637\u0648\u0629 \u0627\u0644\u0632\u0645\u0646\u064a\u0629 <code>maxTimeStep<\/code> \u0648\u0646\u0642\u0648\u0645 \u0628\u062a\u0637\u0628\u064a\u0642 \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0628\u0634\u0643\u0644 \u0645\u062a\u0643\u0631\u0631 \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0647\u0630\u0647 \u0627\u0644\u062e\u0637\u0648\u0629 \u0627\u0644\u0632\u0645\u0646\u064a\u0629 \u0627\u0644\u0645\u062d\u062f\u0648\u062f\u0629. \u0641\u064a \u0643\u0644 \u062a\u0643\u0631\u0627\u0631 \u0646\u0642\u0648\u0645 \u0628\u062a\u0642\u0644\u064a\u0635 \u0627\u0644\u0632\u0645\u0646 \u0627\u0644\u0645\u062a\u0628\u0642\u064a \u0648\u0641\u0642 \u0647\u0630\u0647 \u0627\u0644\u062e\u0637\u0648\u0629\u060c \u0648\u0639\u0646\u062f\u0645\u0627 \u064a\u0635\u0628\u062d \u0627\u0644\u0632\u0645\u0646 \u0627\u0644\u0645\u062a\u0628\u0642\u064a \u0623\u0635\u063a\u0631 \u0645\u0646 \u0627\u0644\u062d\u062f \u0623\u0639\u0644\u0649 \u0644\u0644\u062e\u0637\u0648\u0629 \u0627\u0644\u0632\u0645\u0646\u064a\u0629\u060c \u0646\u0642\u0648\u0645 \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645\u0647 \u0628\u0634\u0643\u0644 \u0645\u0628\u0627\u0634\u0631.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u0627\u0644\u062a\u0645\u062b\u064a\u0644 \u0627\u0644\u0645\u0631\u0626\u064a<\/h2>\n\n\n\n<p>\u064a\u0633\u0645\u062d \u0627\u0644\u0643\u0648\u062f \u0627\u0644\u0628\u0631\u0645\u062c\u064a \u0627\u0644\u0633\u0627\u0628\u0642 \u0628\u062d\u0633\u0627\u0628 \u0645\u0648\u0636\u0639 \u0627\u0644\u062c\u0633\u064a\u0645 \u0641\u064a \u0623\u064a \u0644\u062d\u0638\u0629 \u0632\u0645\u0646\u064a\u0629 \u0645\u0646 \u062e\u0644\u0627\u0644 \u0627\u0633\u062a\u062f\u0639\u0627\u0621 \u0627\u0644\u062a\u0627\u0628\u0639 <code>advance<\/code> \u0645\u0631\u0629 \u0648\u0627\u062d\u062f\u0629 \u0623\u0648 \u0623\u0643\u062b\u0631 \u0648\u0642\u0631\u0627\u0621\u0629 \u0642\u064a\u0645\u0629 \u0627\u0644\u0645\u062a\u062d\u0648\u0644 <code>position<\/code>. \u0641\u064a \u0645\u0639\u0638\u0645 \u0627\u0644\u062a\u0637\u0628\u064a\u0642\u0627\u062a \u0627\u0644\u0639\u0645\u0644\u064a\u0629 \u0641\u0625\u0646 \u0647\u062f\u0641 \u0627\u0644\u0645\u062d\u0627\u0643\u0627\u0629 \u0647\u0648 \u0641\u0642\u0637 \u062d\u0633\u0627\u0628 \u0645\u062b\u0644 \u0647\u0630\u0647 \u0627\u0644\u0642\u064a\u0645 \u0648\u0627\u0633\u062a\u062e\u062f\u0627\u0645\u0647\u0627 \u0641\u064a \u0645\u0643\u0627\u0646 \u0623\u062e\u0631 \u0645\u062b\u0644 \u0645\u0642\u0627\u0631\u0646\u062a\u0647\u0627 \u0645\u0639 \u0627\u0644\u062a\u062c\u0631\u0628\u0629 \u0623\u0648 \u0627\u0633\u062a\u062e\u062f\u0627\u0645\u0647\u0627 \u0641\u064a \u062d\u0633\u0627\u0628\u0627\u062a \u0644\u0627\u062d\u0642\u0629. \u0648\u0644\u0643\u0646 \u0641\u064a \u0643\u062b\u064a\u0631 \u0645\u0646 \u0627\u0644\u0623\u062d\u064a\u0627\u0646\u060c \u0646\u0631\u064a\u062f \u062a\u0645\u062b\u064a\u0644 \u0628\u0635\u0631\u064a \u0644\u0647\u0630\u0647 \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a \u064a\u0633\u0645\u062d \u0644\u0646\u0627 \u0628\u0641\u0647\u0645 \u0623\u0639\u0645\u0642 \u0644\u0633\u0644\u0648\u0643 \u0627\u0644\u0646\u0638\u0627\u0645 \u0642\u064a\u062f \u0627\u0644\u0645\u062d\u0627\u0643\u0627\u0629. \u062a\u062f\u0639\u0649 \u0647\u0630\u0647 \u0627\u0644\u062e\u0637\u0648\u0629 \u0628\u0640&#8221;<a href=\"https:\/\/ar.wikipedia.org\/wiki\/%D8%AA%D9%85%D8%AB%D9%8A%D9%84_%D9%85%D8%B1%D8%A6%D9%8A_(%D8%B1%D8%B3%D9%88%D9%85%D9%8A%D8%A7%D8%AA)\">\u0627\u0644\u062a\u0645\u062b\u064a\u0644 \u0627\u0644\u0645\u0631\u0626\u064a<\/a>&#8221; (<a href=\"https:\/\/en.wikipedia.org\/wiki\/Visualization_(graphics)\">Visulatization<\/a>).<\/p>\n\n\n\n<p>\u0645\u0646 \u0623\u0628\u0633\u0637 \u0623\u0634\u0643\u0627\u0644 \u0627\u0644\u062a\u0645\u062b\u064a\u0644 \u0627\u0644\u0645\u0631\u0626\u064a \u0647\u0648 \u0631\u0633\u0645 \u0645\u062e\u0637\u0637 \u0628\u064a\u0627\u0646\u064a \u064a\u0631\u0628\u0637 \u0645\u062a\u063a\u064a\u0631\u0627\u062a \u0627\u0644\u0645\u062d\u0627\u0643\u0627\u0629 \u0645\u0639 \u0628\u0639\u0636\u0647\u0627. \u0641\u064a \u0627\u0644\u0645\u062d\u0627\u0643\u0627\u0629 \u0627\u0644\u062d\u0627\u0644\u064a\u0629\u060c \u064a\u062a\u0645\u062b\u0644 \u0630\u0644\u0643 \u0628\u0645\u062e\u0637\u0637 \u064a\u0648\u0636\u062d \u0645\u0648\u0636\u0639 \u0627\u0644\u062c\u0633\u064a\u0645 \\(x(t)\\) \u0641\u064a \u0644\u062d\u0638\u0627\u062a \u0632\u0645\u0646\u064a\u0629 \u0645\u062e\u062a\u0644\u0641\u0629 \\(t\\):<\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"631\" height=\"385\" src=\"https:\/\/entangled-thoughts.com\/ar\/wp-content\/uploads\/2025\/03\/example_plot.svg\" alt=\"\" class=\"wp-image-892\" style=\"width:570px;height:auto\"\/><figcaption class=\"wp-element-caption\"><strong>\u0631\u0633\u0645 \u0628\u064a\u0627\u0646\u064a \u0644\u0645\u062e\u0631\u062c\u0627\u062a \u0645\u062d\u0627\u0643\u0627\u0629 \u062c\u0633\u064a\u0645 \u0628\u0643\u062a\u0644\u0629 \\(m=0.5\\) \u0648\u0627\u0632\u0627\u062d\u0629 \u0627\u0628\u062a\u062f\u0627\u0626\u064a\u0629 \\(x_0=2\\) \u0645\u0631\u062a\u0628\u0637 \u0628\u0646\u0627\u0628\u0636 \u0630\u0648 \u062b\u0627\u0628\u062a \u0635\u0644\u0627\u0628\u0629 \\(k=5\\) \u0648\u062b\u0627\u0628\u062a \u062a\u062e\u0645\u064a\u062f \\(c=0.1\\)<\/strong><\/figcaption><\/figure>\n\n\n\n<p>\u0647\u0646\u0627\u0644\u0643 \u062a\u0642\u0646\u064a\u0627\u062a \u0623\u0643\u062b\u0631 \u062a\u0639\u0642\u064a\u062f\u0627 \u0641\u064a \u0627\u0644\u062a\u0645\u062b\u064a\u0644 \u0627\u0644\u0645\u0631\u0626\u064a \u0645\u062b\u0644 \u062a\u0642\u0646\u064a\u0629 <a href=\"https:\/\/ar.wikipedia.org\/wiki\/%D8%AA%D8%AD%D8%B1%D9%8A%D9%83_%D8%AD%D8%A7%D8%B3%D9%88%D8%A8%D9%8A\">\u0627\u0644\u062a\u062d\u0631\u064a\u0643 \u0627\u0644\u062d\u0627\u0633\u0648\u0628\u064a<\/a> (<a href=\"https:\/\/en.wikipedia.org\/wiki\/Computer_animation\">Computer Animation<\/a>) \u0627\u0644\u0645\u0633\u062a\u062e\u062f\u0645\u0629 \u0641\u064a \u0627\u0644\u0628\u0631\u0646\u0627\u0645\u062c \u0627\u0644\u0645\u0648\u062c\u0648\u062f \u0641\u064a \u0623\u0639\u0644\u0649 \u0627\u0644\u0635\u0641\u062d\u0629. \u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u062a\u0642\u0646\u064a\u0629 \u064a\u062a\u0645 \u0628\u0646\u0627\u0621 \u0646\u0645\u0648\u0630\u062c \u062b\u0646\u0627\u0626\u064a \u0623\u0648 \u062b\u0644\u0627\u062b\u064a \u0627\u0644\u0623\u0628\u0639\u0627\u062f \u0648\u062a\u062d\u0631\u064a\u0643\u0647 \u0648\u0641\u0642 \u0645\u062e\u0631\u062c\u0627\u062a \u0627\u0644\u0645\u062d\u0627\u0643\u0627\u0629 \u0627\u0644\u0641\u064a\u0632\u064a\u0627\u0626\u064a\u0629 \u0645\u0646 \u0623\u062c\u0644 \u062a\u0648\u0644\u064a\u062f \u0635\u0648\u0631 \u0645\u062a\u062d\u0631\u0643\u0629 \u062a\u0638\u0647\u0631 \u0627\u0644\u0646\u0638\u0627\u0645 \u0627\u0644\u0645\u0631\u0627\u062f \u0645\u062d\u0627\u0643\u0627\u062a\u0647 \u0628\u0634\u0643\u0644 \u0648\u0627\u0642\u0639\u064a.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u0627\u0644\u0643\u0648\u062f \u0627\u0644\u0628\u0631\u0645\u062c\u064a \u0644\u0644\u062a\u062d\u0631\u064a\u0643 \u0627\u0644\u062d\u0627\u0633\u0648\u0628\u064a<\/h2>\n\n\n\n<p>\u0645\u0646 \u0623\u062c\u0644 \u0628\u0646\u0627\u0621 \u0627\u0644\u0645\u062d\u0627\u0643\u0627\u0629 \u0627\u0644\u062a\u0641\u0627\u0639\u0644\u064a\u0629 \u0623\u0639\u0644\u0627\u0647\u060c \u0642\u0645\u0646\u0627 \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0645\u0643\u062a\u0628\u0629 <a href=\"https:\/\/threejs.org\/\">threejs<\/a> \u0627\u0644\u0628\u0631\u0645\u062c\u064a\u0629 \u0644\u0644\u0646\u0645\u0630\u062c\u0629 \u062b\u0644\u0627\u062b\u064a\u0629 \u0627\u0644\u0623\u0628\u0639\u0627\u062f.\u0634\u0631\u062d \u0623\u0633\u0627\u0633\u064a\u0627\u062a \u0643\u064a\u0641\u064a\u0629 \u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0647\u0630\u0647 \u0627\u0644\u0645\u0643\u062a\u0628\u0629 \u0648\u0628\u0646\u0627\u0621 \u0627\u0644\u0646\u0645\u0648\u0630\u062c \u062b\u0644\u0627\u062b\u064a \u0627\u0644\u0623\u0628\u0639\u0627\u062f \u064a\u062a\u062c\u0627\u0648\u0632 \u0646\u0637\u0627\u0642 \u0647\u0630\u0647 \u0627\u0644\u0645\u0642\u0627\u0644\u0629 \u0648\u0644\u0643\u0646 \u0628\u0627\u0645\u0643\u0627\u0646\u0643 \u0627\u0644\u062a\u062d\u0642\u0642 \u0645\u0646 <a href=\"https:\/\/github.com\/entangled-thoughts\/mass-spring-damper\" target=\"_blank\" rel=\"noreferrer noopener\">\u0627\u0644\u0643\u0648\u062f \u0627\u0644\u0645\u0635\u062f\u0631\u064a \u0628\u0627\u0644\u0643\u0627\u0645\u0644 \u0647\u0646\u0627<\/a>. \u0633\u0646\u0631\u0643\u0632 \u0641\u064a\u0645\u0627 \u064a\u0644\u064a \u0639\u0644\u0649 \u0645\u0642\u062a\u0637\u0641 \u0645\u0646 \u0627\u0644\u0643\u0648\u062f \u0627\u0644\u0628\u0631\u0645\u062c\u064a \u064a\u0648\u0636\u062d \u0628\u0639\u0636 \u0627\u0644\u0646\u0642\u0627\u0637 \u0627\u0644\u0623\u0633\u0627\u0633\u064a\u0629 \u0627\u0644\u0634\u0627\u0626\u0639\u0629 \u0641\u064a \u0645\u062b\u0644 \u0628\u0631\u0627\u0645\u062c \u0627\u0644\u062a\u062d\u0631\u064a\u0643 \u0627\u0644\u062d\u0627\u0633\u0648\u0628\u064a \u0647\u0630\u0647 \u0627\u0644\u0642\u0627\u0626\u0645\u0629 \u0639\u0644\u0649 \u0627\u0644\u0641\u064a\u0632\u064a\u0627\u0621:<\/p>\n\n\n\n<div class=\"wp-block-kevinbatdorf-code-block-pro cbp-has-line-numbers\" data-code-block-pro-font-family=\"Code-Pro-JetBrains-Mono\" style=\"font-size:.875rem;font-family:Code-Pro-JetBrains-Mono,ui-monospace,SFMono-Regular,Menlo,Monaco,Consolas,monospace;--cbp-line-number-color:#D4D4D4;--cbp-line-number-width:calc(2 * 0.6 * .875rem);line-height:1.25rem;--cbp-tab-width:2;tab-size:var(--cbp-tab-width, 2)\"><span role=\"button\" tabindex=\"0\" data-code=\"\/\/ Create the physics simulator with some initial parameters\nconst params = { mass: 0.5, stifness: 5.0, dampness: 0.0, displacement: 2.0 };\nlet simulation = new MassSpringDamperPhysics(params.mass, params.stifness, params.dampness, params.displacement);\n\n\/\/Create the 3D model and add it to the scene\nconst model = createMassSpring3DModel();\nscene.add(model);\n\n\/\/ Create a clock to keep track of simulation time\nconst clock = new THREE.Clock();\n\n\/\/ The animate function will be called every frame\nfunction animate() {\n    \/\/ Advance the simulation based on the time elapsed since the last frame\n    simulation.advance(clock.getDelta());\n    \/\/ Update the model's stretch based on the particle's position\n    model.setStretch(simulation.position);\n    \/\/ Update the camera controls and render the scene\n    cameraControls.update();\n    renderer.render(scene, camera);\n}\n\/\/ Setup the animation loop\nrenderer.setAnimationLoop(animate);\n\" style=\"color:#D4D4D4;display:none\" aria-label=\"Copy\" class=\"code-block-pro-copy-button\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" style=\"width:24px;height:24px\" fill=\"none\" viewBox=\"0 0 24 24\" stroke=\"currentColor\" stroke-width=\"2\"><path class=\"with-check\" stroke-linecap=\"round\" stroke-linejoin=\"round\" d=\"M9 5H7a2 2 0 00-2 2v12a2 2 0 002 2h10a2 2 0 002-2V7a2 2 0 00-2-2h-2M9 5a2 2 0 002 2h2a2 2 0 002-2M9 5a2 2 0 012-2h2a2 2 0 012 2m-6 9l2 2 4-4\"><\/path><path class=\"without-check\" stroke-linecap=\"round\" stroke-linejoin=\"round\" d=\"M9 5H7a2 2 0 00-2 2v12a2 2 0 002 2h10a2 2 0 002-2V7a2 2 0 00-2-2h-2M9 5a2 2 0 002 2h2a2 2 0 002-2M9 5a2 2 0 012-2h2a2 2 0 012 2\"><\/path><\/svg><\/span><pre class=\"shiki dark-plus\" style=\"background-color: #1E1E1E\" tabindex=\"0\"><code><span class=\"line\"><span style=\"color: #6A9955\">\/\/ Create the physics simulator with some initial parameters<\/span><\/span>\n<span class=\"line\"><span style=\"color: #569CD6\">const<\/span><span style=\"color: #D4D4D4\"> <\/span><span style=\"color: #4FC1FF\">params<\/span><span style=\"color: #D4D4D4\"> = { <\/span><span style=\"color: #9CDCFE\">mass:<\/span><span style=\"color: #D4D4D4\"> <\/span><span style=\"color: #B5CEA8\">0.5<\/span><span style=\"color: #D4D4D4\">, <\/span><span style=\"color: #9CDCFE\">stifness:<\/span><span style=\"color: #D4D4D4\"> <\/span><span style=\"color: #B5CEA8\">5.0<\/span><span style=\"color: #D4D4D4\">, <\/span><span style=\"color: #9CDCFE\">dampness:<\/span><span style=\"color: #D4D4D4\"> <\/span><span style=\"color: #B5CEA8\">0.0<\/span><span style=\"color: #D4D4D4\">, <\/span><span style=\"color: #9CDCFE\">displacement:<\/span><span style=\"color: #D4D4D4\"> <\/span><span style=\"color: #B5CEA8\">2.0<\/span><span style=\"color: #D4D4D4\"> };<\/span><\/span>\n<span class=\"line\"><span style=\"color: #569CD6\">let<\/span><span style=\"color: #D4D4D4\"> <\/span><span style=\"color: #9CDCFE\">simulation<\/span><span style=\"color: #D4D4D4\"> = <\/span><span style=\"color: #569CD6\">new<\/span><span style=\"color: #D4D4D4\"> <\/span><span style=\"color: #DCDCAA\">MassSpringDamperPhysics<\/span><span style=\"color: #D4D4D4\">(<\/span><span style=\"color: #9CDCFE\">params<\/span><span style=\"color: #D4D4D4\">.<\/span><span style=\"color: #9CDCFE\">mass<\/span><span style=\"color: #D4D4D4\">, <\/span><span style=\"color: #9CDCFE\">params<\/span><span style=\"color: #D4D4D4\">.<\/span><span style=\"color: #9CDCFE\">stifness<\/span><span style=\"color: #D4D4D4\">, <\/span><span style=\"color: #9CDCFE\">params<\/span><span style=\"color: #D4D4D4\">.<\/span><span style=\"color: #9CDCFE\">dampness<\/span><span style=\"color: #D4D4D4\">, <\/span><span style=\"color: #9CDCFE\">params<\/span><span style=\"color: #D4D4D4\">.<\/span><span style=\"color: #9CDCFE\">displacement<\/span><span style=\"color: #D4D4D4\">);<\/span><\/span>\n<span class=\"line\"><\/span>\n<span class=\"line\"><span style=\"color: #6A9955\">\/\/Create the 3D model and add it to the scene<\/span><\/span>\n<span class=\"line\"><span style=\"color: #569CD6\">const<\/span><span style=\"color: #D4D4D4\"> <\/span><span style=\"color: #4FC1FF\">model<\/span><span style=\"color: #D4D4D4\"> = <\/span><span style=\"color: #DCDCAA\">createMassSpring3DModel<\/span><span style=\"color: #D4D4D4\">();<\/span><\/span>\n<span class=\"line\"><span style=\"color: #9CDCFE\">scene<\/span><span style=\"color: #D4D4D4\">.<\/span><span style=\"color: #DCDCAA\">add<\/span><span style=\"color: #D4D4D4\">(<\/span><span style=\"color: #9CDCFE\">model<\/span><span style=\"color: #D4D4D4\">);<\/span><\/span>\n<span class=\"line\"><\/span>\n<span class=\"line\"><span style=\"color: #6A9955\">\/\/ Create a clock to keep track of simulation time<\/span><\/span>\n<span class=\"line\"><span style=\"color: #569CD6\">const<\/span><span style=\"color: #D4D4D4\"> <\/span><span style=\"color: #4FC1FF\">clock<\/span><span style=\"color: #D4D4D4\"> = <\/span><span style=\"color: #569CD6\">new<\/span><span style=\"color: #D4D4D4\"> <\/span><span style=\"color: #4FC1FF\">THREE<\/span><span style=\"color: #D4D4D4\">.<\/span><span style=\"color: #DCDCAA\">Clock<\/span><span style=\"color: #D4D4D4\">();<\/span><\/span>\n<span class=\"line\"><\/span>\n<span class=\"line\"><span style=\"color: #6A9955\">\/\/ The animate function will be called every frame<\/span><\/span>\n<span class=\"line\"><span style=\"color: #569CD6\">function<\/span><span style=\"color: #D4D4D4\"> <\/span><span style=\"color: #DCDCAA\">animate<\/span><span style=\"color: #D4D4D4\">() {<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">    <\/span><span style=\"color: #6A9955\">\/\/ Advance the simulation based on the time elapsed since the last frame<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">    <\/span><span style=\"color: #9CDCFE\">simulation<\/span><span style=\"color: #D4D4D4\">.<\/span><span style=\"color: #DCDCAA\">advance<\/span><span style=\"color: #D4D4D4\">(<\/span><span style=\"color: #9CDCFE\">clock<\/span><span style=\"color: #D4D4D4\">.<\/span><span style=\"color: #DCDCAA\">getDelta<\/span><span style=\"color: #D4D4D4\">());<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">    <\/span><span style=\"color: #6A9955\">\/\/ Update the model&#39;s stretch based on the particle&#39;s position<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">    <\/span><span style=\"color: #9CDCFE\">model<\/span><span style=\"color: #D4D4D4\">.<\/span><span style=\"color: #DCDCAA\">setStretch<\/span><span style=\"color: #D4D4D4\">(<\/span><span style=\"color: #9CDCFE\">simulation<\/span><span style=\"color: #D4D4D4\">.<\/span><span style=\"color: #9CDCFE\">position<\/span><span style=\"color: #D4D4D4\">);<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">    <\/span><span style=\"color: #6A9955\">\/\/ Update the camera controls and render the scene<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">    <\/span><span style=\"color: #9CDCFE\">cameraControls<\/span><span style=\"color: #D4D4D4\">.<\/span><span style=\"color: #DCDCAA\">update<\/span><span style=\"color: #D4D4D4\">();<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">    <\/span><span style=\"color: #9CDCFE\">renderer<\/span><span style=\"color: #D4D4D4\">.<\/span><span style=\"color: #DCDCAA\">render<\/span><span style=\"color: #D4D4D4\">(<\/span><span style=\"color: #9CDCFE\">scene<\/span><span style=\"color: #D4D4D4\">, <\/span><span style=\"color: #9CDCFE\">camera<\/span><span style=\"color: #D4D4D4\">);<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D4D4D4\">}<\/span><\/span>\n<span class=\"line\"><span style=\"color: #6A9955\">\/\/ Setup the animation loop<\/span><\/span>\n<span class=\"line\"><span style=\"color: #9CDCFE\">renderer<\/span><span style=\"color: #D4D4D4\">.<\/span><span style=\"color: #DCDCAA\">setAnimationLoop<\/span><span style=\"color: #D4D4D4\">(<\/span><span style=\"color: #9CDCFE\">animate<\/span><span style=\"color: #D4D4D4\">);<\/span><\/span>\n<span class=\"line\"><\/span><\/code><\/pre><\/div>\n\n\n\n<p><\/p>\n\n\n\n<p>\u0628\u062f\u0627\u064a\u0629 \u0646\u0642\u0648\u0645 \u0628\u0627\u0646\u0634\u0627\u0621 \u0627\u0644\u0645\u062d\u0627\u0643\u064a \u0627\u0644\u0641\u064a\u0632\u064a\u0627\u0626\u064a \u0627\u0644\u0630\u064a \u0637\u0648\u0631\u0646\u0627\u0647 \u0641\u064a \u0642\u0633\u0645 \u0633\u0627\u0628\u0642 \u0648\u062a\u0647\u064a\u0626\u062a\u0647 \u0628\u0645\u062f\u062e\u0644\u0627\u062a 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\u0647\u0646\u0627\u0644\u0643 \u062d\u0644\u0642\u0629 \u0645\u0633\u062a\u0645\u0631\u0629 \u064a\u062a\u0645 \u062e\u0644\u0627\u0644\u0647\u0627 \u0627\u0633\u062a\u062f\u0639\u0627\u0621 \u062a\u0627\u0628\u0639 \u0628\u0631\u0645\u062c\u064a \u0628\u0634\u0643\u0644 \u062f\u0648\u0631\u064a \u0645\u0646 \u0625\u0639\u0627\u062f\u0629 \u0631\u0633\u0645 \u0627\u0644\u0635\u0648\u0631\u0629 \u0627\u0644\u0638\u0627\u0647\u0631\u0629 \u0639\u0644\u0649 \u0627\u0644\u0634\u0627\u0634\u0629. \u0627\u0644\u0633\u0637\u0631 23 \u0641\u064a \u0627\u0644\u0643\u0648\u062f \u064a\u062e\u0628\u0631 \u0645\u0643\u062a\u0628\u0629 threejs \u0623\u0646 \u0647\u0630\u0627 \u062a\u0627\u0628\u0639 \u0647\u0648 <code>animate<\/code>.<\/p>\n\n\n\n<p> \u0636\u0645\u0646 \u0627\u0644\u062a\u0627\u0628\u0639 \u0627\u0644\u0628\u0631\u0645\u062c\u064a <code>animate<\/code>\u060c \u0646\u0642\u0648\u0645 \u0628\u0627\u0633\u062a\u062f\u0639\u0627\u0621 \u0627\u0644\u062a\u0627\u0628\u0639 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