A) \[\frac{1}{3}s\]
B) \[\frac{1}{2}s\]
C) \[\frac{2}{3}s\]
D) \[\frac{1}{6}s\]
Correct Answer: A
Solution :
The displacement equation for \[SHM\] is \[y=a\sin \omega t\] where \[\omega \] is angular velocity \[\left( \omega =\frac{2\pi }{T} \right)\] and a the amplitude. Given, \[y=\frac{a}{2},\,\,t=\frac{t}{2}\] \[\therefore \] \[\frac{a}{2}=a\,\,\sin \frac{2\pi t}{4}\] \[\Rightarrow \] \[\frac{1}{2}=\sin \frac{\pi t}{2}\] \[\therefore \] \[\sin \frac{\pi }{6}=\sin \frac{\pi t}{2}\] \[\Rightarrow \] \[\frac{\pi }{6}=\frac{\pi t}{2}\] \[\Rightarrow \] \[t=\frac{1}{3}s\]
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