A simple harmonic oscillator has an amplitude a and time period $T$. The time required by it to travel from $x = a$ to $x = \frac{a }{2}$ is
AIPMT 1992, Medium
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(a) It is required to calculate the time from extreme position.
Hence, in this case equation for displacement of particle can be written as $x = a\sin (\omega \,t + \frac{\pi }{2}) = a\cos \omega \,t$
Hence, in this case equation for displacement of particle can be written as $x = a\sin (\omega \,t + \frac{\pi }{2}) = a\cos \omega \,t$
==> $\frac{a}{2} = a\cos \omega \,t$
==> $\omega \,t = \frac{\pi }{3}$
==> $\frac{{2\pi }}{T}.t = \frac{\pi }{3}$
==> $t = \frac{T}{6}$
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