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  4. The periodic time of a particle executing SHM is 4 s. The time taken by it to go from its mean position to half the maximum displacement (amplitude) is

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Q. The periodic time of a particle executing SHM is 4 s. The time taken by it to go from its mean position to half the maximum displacement (amplitude) is

CMC MedicalCMC Medical 2012

Solution:

$ y=A\,\,\sin \left( \frac{2\pi }{T} \right)t $ $ \Rightarrow $ $ \frac{A}{2}=A\,\,\sin \left( \frac{2\pi }{4} \right)t $ $ \Rightarrow $ $ \frac{\pi t}{2}=\frac{\pi }{6}\Rightarrow \,t=\frac{1}{3}s $