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

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أ- من الرسم البياني يمكن ملاحظة أنّه في اللحظة $\mathrm{<span\; class=""\; id="yui\_3\_17\_2\_1\_1750798204155\_3708"\; style="font-size:\; large;\; color:\; rgb(0,\; 61,\; 245);">t</span>}<span\; class=""\; id="yui\_3\_17\_2\_1\_1750798204155\_3709"\; style="font-size:\; large;\; color:\; rgb(0,\; 61,\; 245);">=</span>\mathrm{<span\; class=""\; id="yui\_3\_17\_2\_1\_1750798204155\_3710"\; style="font-size:\; large;\; color:\; rgb(0,\; 61,\; 245);">0</span>}\mathrm{<span\; class=""\; id="yui\_3\_17\_2\_1\_1750798204155\_3711"\; style="font-size:\; large;\; color:\; rgb(0,\; 61,\; 245);">s</span>}$t = 0st=0s يبدأ الجسم بالحركة من نقطة الطرف الموجبة، وفي اللحظة $\mathrm{<span\; class=""\; id="yui\_3\_17\_2\_1\_1750798204155\_3714"\; style="font-size:\; large;\; color:\; rgb(0,\; 61,\; 245);">t</span>}<span\; class=""\; id="yui\_3\_17\_2\_1\_1750798204155\_3715"\; style="font-size:\; large;\; color:\; rgb(0,\; 61,\; 245);">=</span>\mathrm{<span\; class=""\; id="yui\_3\_17\_2\_1\_1750798204155\_3716"\; style="font-size:\; large;\; color:\; rgb(0,\; 61,\; 245);">1.5</span>}\mathrm{<span\; class=""\; id="yui\_3\_17\_2\_1\_1750798204155\_3717"\; style="font-size:\; large;\; color:\; rgb(0,\; 61,\; 245);">s</span>}$t = 1.5st=1.5s يصل إلى نقطة الطرف السالبة، وسعة الاهتزاز هي 2 متر.

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د- من دالة السرعة بدلالة الزمن «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»V«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#969;A«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»sin«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#969;t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#1012;«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«/math» يمكن تحديد أن مقدار السرعة العظمى هو:

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نحسب مقدار السرعة العظمى:

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ה-  من دالة التسارع بدلالة الزمن «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»a«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«msup»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#969;«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msup»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»A«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»cos«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#969;t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#1012;«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«/math» يمكن تحديد أن مقدار التسارع الأقصى هو:

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