حل التدريبات العملية: الحركة التوافقية البسيطة في نابض أفقي وبندول بسيط

5.6

نكتب تعبيرًا للسرعة العظمى للصندوق في المنظومتين الثالثة والرابعة:

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نُقارن بين تعبيري السرعتين العُظمَيَين ونُعبّر عن نسبة السعتين:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨20px¨»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»V«/mi»«msub mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»max«/mi»«mn mathvariant=¨bold¨»3«/mn»«/msub»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»V«/mi»«msub mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»max«/mi»«mn mathvariant=¨bold¨»4«/mn»«/msub»«/msub»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«msqrt mathcolor=¨#0000FF¨»«mfrac»«msub»«mi mathvariant=¨bold¨»k«/mi»«mn mathvariant=¨bold¨»3«/mn»«/msub»«msub»«mi mathvariant=¨bold¨»m«/mi»«mn mathvariant=¨bold¨»3«/mn»«/msub»«/mfrac»«/msqrt»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»A«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»3«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«msqrt mathcolor=¨#0000FF¨»«mfrac»«msub»«mi mathvariant=¨bold¨»k«/mi»«mn mathvariant=¨bold¨»4«/mn»«/msub»«msub»«mi mathvariant=¨bold¨»m«/mi»«mn mathvariant=¨bold¨»4«/mn»«/msub»«/mfrac»«/msqrt»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»A«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»4«/mn»«/msub»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mfrac mathcolor=¨#0000FF¨»«msub»«mi mathvariant=¨bold¨»A«/mi»«mn mathvariant=¨bold¨»4«/mn»«/msub»«msub»«mi mathvariant=¨bold¨»A«/mi»«mn mathvariant=¨bold¨»3«/mn»«/msub»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«msqrt»«mfrac»«msub»«mi mathvariant=¨bold¨»k«/mi»«mn mathvariant=¨bold¨»3«/mn»«/msub»«msub»«mi mathvariant=¨bold¨»m«/mi»«mn mathvariant=¨bold¨»3«/mn»«/msub»«/mfrac»«/msqrt»«msqrt»«mfrac»«msub»«mi mathvariant=¨bold¨»k«/mi»«mn mathvariant=¨bold¨»4«/mn»«/msub»«msub»«mi mathvariant=¨bold¨»m«/mi»«mn mathvariant=¨bold¨»4«/mn»«/msub»«/mfrac»«/msqrt»«/mfrac»«/mstyle»«/math»

كتلة الصندوق متساوية، لذلك فهي تختزل:

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