A) \[A_{1}^{2}\omega _{1}^{2}=A_{2}^{2}\omega _{2}^{2}=A_{3}^{2}{{\omega }^{2}}\]
B) \[A_{1}^{2}{{\omega }_{1}}=A_{2}^{2}{{\omega }_{1}}=A_{3}^{2}{{\omega }_{3}}\]
C) \[{{A}_{1}}\omega _{1}^{2}={{A}_{2}}\omega _{2}^{2},\,\,{{A}_{3}}\omega _{3}^{2}\]
D) \[{{A}_{1}}{{\omega }_{1}}={{A}_{2}}{{\omega }_{2}}={{A}_{3}}{{\omega }_{3}}\]
Correct Answer: D
Solution :
Rate of change of displacement is known as velocity. The equation for displacement \[(y)\] of a body in SHM with angular velocity\[\omega \]is given by \[y=a\sin \omega t\] where a is amplitude velocity \[v=\] rate of change of displacement\[=\frac{dy}{dt}\] \[V=\frac{dy}{dt}=\frac{d}{dt}(a\sin \omega t)=a\omega \cos \omega t\] Given,\[{{v}_{1}}={{v}_{2}}={{v}_{3}}\]and\[{{a}_{1}}={{A}_{1}},\,\,{{a}_{2}}={{A}_{2}}\] \[{{a}_{3}}={{A}_{3}}\] \[{{A}_{1}}{{\omega }_{1}}={{A}_{2}}{{\omega }_{2}}={{A}_{3}}{{\omega }_{3}}\]
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