A) \[\frac{T}{4}\]
B) \[\frac{T}{8}\]
C) \[\frac{T}{12}\]
D) \[\frac{T}{2}\]
Correct Answer: C
Solution :
Let displacement equation of particle executing SHM is \[\operatorname{y} \,= \,a\,\,sin\,\omega t\] As particle travels half of the amplitude from the equilibrium position, so \[y=\frac{a}{2}\] Therefore, \[\frac{a}{2}=a\sin \,\omega t\] \[\sin \,\omega t\,\,=\,\,\frac{1}{2}=\sin \,\frac{\pi }{6}\] \[\omega t=\frac{\pi }{6}\] or \[t=\frac{\pi }{6\omega }\] or \[t=\frac{\pi }{6\left( \frac{2\pi }{T} \right)}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\left( as\,\,\omega =\frac{2\pi }{T} \right)\] \[t=\frac{T}{12}\] Hence, the particle travels half of the amplitude from the equilibrium in \[\frac{T}{12}\,s\].You need to login to perform this action.
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