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 \[y=a\sin \omega t\] As particle travels half of the amplitude from the equilibrium position, so \[y=\frac{a}{2}\] Therefore, \[\frac{a}{2}=a\sin \omega t\] or \[\sin \omega t=\frac{1}{2}=\sin \frac{\pi }{6}\] or \[\omega t=\frac{\pi }{6}\] or \[t=\frac{\pi }{6\left( \frac{2\pi }{T} \right)}\] \[\left( \text{as}\,\,\omega =\frac{2\pi }{T} \right)\] or \[t=\frac{T}{12}\] Hence, the particle travels half of the amplitude from the equilibrium in\[t=\frac{T}{12}s\].
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