The kinetic energy of a particle executing $S.H.M.$ is $16\, J$ when it is in its mean position. If the amplitude of oscillations is $25\, cm$ and the mass of the particle is $5.12\, kg$, the time period of its oscillation is
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(a) At mean position, the kinetic energy is maximum.
Hence $\frac{1}{2}m{a^2}{\omega ^2} = 16$
On putting the values we get $\omega = 10\; \Rightarrow \;T = \frac{{2\pi }}{\omega } = \frac{\pi }{5}\sec $
Hence $\frac{1}{2}m{a^2}{\omega ^2} = 16$
On putting the values we get $\omega = 10\; \Rightarrow \;T = \frac{{2\pi }}{\omega } = \frac{\pi }{5}\sec $
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