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

8.2

نكتب تعبيرًا لسعة الحركة:

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نُعبّر عن سرعة الجسم في النقطة B بدلالة لطول الخيط $L$L باستخدام دالة السرعة كدالة للزمن:

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يصل الجسم إلى النقطة B بعد ربع زمن دورة. في لحظة بداية الحركة، يكون الجسم في نقطة الطرف الموجب، لذلك فإن قيمة زاوية الطور الابتدائية تساوي صفرًا.

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نُعبّر عن زمن الدورة باستخدام التعبير المناسب لحركة بندول بسيط في زوايا صغيرة:

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نُعبّر عن سرعة الجسم في النقطة B بدلالة لطول الخيط $L$L باستخدام دالة السرعة كدالة للموقع:

نكتب دالة السرعة كدالة للموقع، عندما يكون الجسم في الموضع X=0m.

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نُعبّر عن زمن الدورة باستخدام التعبير المناسب لحركة بندول بسيط في زوايا صغيرة:

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في المرة الأولى التي يمر فيها الجسم في النقطة B، يكون متحركًا بعكس اتجاه الحركة، ولذلك فإن سرعته سالبة «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨18px¨»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»V«/mi»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»B«/mi»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»4773«/mn»«mfrac mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»m«/mi»«mi mathvariant=¨bold¨»s«/mi»«/mfrac»«/mstyle»«/math» .