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{"save":1,"level":1,"time":"50","total":40,"point":5,"segment":[{"id":"4845","test_id":"524","question":"<p>Trong dao \u0111\u1ed9ng \u0111i\u1ec1u hòa, \u0111\u1ed3 th\u1ecb li \u0111\u1ed9 <span class=\"math-tex\">$x$<\/span> theo th\u1eddi gian <span class=\"math-tex\">$t$<\/span> c\u1ee7a v\u1eadt là m\u1ed9t<\/p>","options":["<strong>A.<\/strong> \u0111o\u1ea1n th\u1eb3ng.","<strong>B.<\/strong> \u0111\u01b0\u1eddng th\u1eb3ng.","<strong>C.<\/strong> \u0111\u01b0\u1eddng hình sin.","<strong>D.<\/strong> \u0111\u01b0\u1eddng tròn."],"correct":"3","answer":"<p>Ch\u1ecdn <span style=\"color:#16a085;\"><strong>C.<\/strong> \u0111\u01b0\u1eddng hình sin.<\/span><span style=\"color:#16a085;\"><\/span> <span style=\"color:#16a085;\"><\/span><\/p>","type":"choose","user_id":"131","test":"1","date":"2025-06-08 08:01:04"},{"id":"4857","test_id":"524","question":"<p>M\u1ed9t v\u1eadt nh\u1ecf dao \u0111\u1ed9ng \u0111i\u1ec1u hòa trên qu\u1ef9 \u0111\u1ea1o dài 8 cm. Khi \u0111i qua v\u1ecb trí cân b\u1eb1ng v\u1eadn t\u1ed1c c\u1ee7a v\u1eadt có \u0111\u1ed9 l\u1edbn <span class=\"math-tex\">$40\\pi$<\/span> cm\/s. Ch\u1ecdn m\u1ed1c th\u1eddi gian là lúc v\u1eadt \u0111i qua v\u1ecb trí <span class=\"math-tex\">$2\\sqrt{3}$<\/span> cm theo chi\u1ec1u d\u01b0\u01a1ng. Ph\u01b0\u01a1ng trình dao \u0111\u1ed9ng c\u1ee7a v\u1eadt là<\/p>","options":["<strong>A.<\/strong> <span class=\"math-tex\">$x=4\\cos\\bigg(10\\pi t-\\dfrac{\\pi}{6}\\bigg)\\;cm$<\/span>","<strong>B.<\/strong> <span class=\"math-tex\">$x=4\\cos\\bigg(10\\pi t+\\dfrac{\\pi}{6}\\bigg)\\;cm$<\/span>","<strong>C.<\/strong> <span class=\"math-tex\">$x=2\\cos\\bigg(20\\pi t-\\dfrac{\\pi}{6}\\bigg)\\;cm$<\/span>","<strong>D.<\/strong> <span class=\"math-tex\">$x=2\\cos\\bigg(20\\pi t+\\dfrac{\\pi}{6}\\bigg)\\;cm$<\/span>"],"correct":"1","answer":"<p>Ch\u1ecdn <span style=\"color:#16a085;\"><strong>A.<\/strong> <span class=\"math-tex\">$x=4\\cos\\bigg(10\\pi t-\\dfrac{\\pi}{6}\\bigg)\\;cm$<\/span>.<\/span><\/p><p>Ph\u01b0\u01a1ng trình dao \u0111\u1ed9ng \u0111i\u1ec1u hòa c\u1ee7a v\u1eadt có d\u1ea1ng: <span class=\"math-tex\">$x=A\\cos(\\omega t+\\varphi)$<\/span>.<\/p><p>Biên \u0111\u1ed9 dao \u0111\u1ed9ng <span class=\"math-tex\">$A=\\dfrac{L}{2}=\\dfrac{8}{2}=4\\;cm$<\/span>.<\/p><p>Khi \u0111i qua v\u1ecb trí cân b\u1eb1ng v\u1eadn t\u1ed1c c\u1ee7a v\u1eadt có \u0111\u1ed9 l\u1edbn <span class=\"math-tex\">$40\\pi$<\/span> cm\/s nên<\/p><p> <span class=\"math-tex\">$|v_{max}|=\\omega A$<\/span> ⇒ <span class=\"math-tex\">$\\omega=|v_{max}|:A=40\\pi:4=10\\pi$<\/span> (rad\/s).<\/p><p>Vì v\u1edbi t = 0, v\u1eadt \u0111i qua v\u1ecb trí <span class=\"math-tex\">$2\\sqrt{3}$<\/span> cm theo chi\u1ec1u d\u01b0\u01a1ng nên <span class=\"math-tex\">$\\begin{cases}2\\sqrt{3}=4\\cos(10\\pi.0+\\varphi)\\\\v>0\\end{cases}$<\/span><\/p><p>Suy ra <span class=\"math-tex\">$\\begin{cases}\\cos\\varphi=\\dfrac{\\sqrt{3}}{2}\\\\\\sin\\varphi<0\\end{cases}$<\/span> ⇔ <span class=\"math-tex\">$\\varphi=-\\dfrac{\\pi}{6}$<\/span>.<\/p><p>V\u1eady ph\u01b0\u01a1ng trình dao \u0111\u1ed9ng \u0111i\u1ec1u hòa c\u1ee7a v\u1eadt là <span class=\"math-tex\">$x=4\\cos\\bigg(10\\pi t-\\dfrac{\\pi}{6}\\bigg)$<\/span> (cm).<\/p>","type":"choose","user_id":"131","test":"1","date":"2025-06-08 08:35:43"}]}