The kinetic energy of a particle executing S. | vedclass

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(A) At the mean position,the kinetic energy of a particle in $S.H.M.$ is maximum and is given by $K_{max} = \frac{1}{2} m \omega^2 A^2 = 16 \ J$.Given

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$\frac{\pi}{5} \ s$

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(A) At the mean position,the kinetic energy of a particle in $S.H.M.$ is maximum and is given by $K_{max} = \frac{1}{2} m \omega^2 A^2 = 16 \ J$.Given: mass $m = 5.12 \ kg$,amplitude $A = 25 \ cm = 0.25 \ m = \frac{1}{4} \ m$.Substituting the values: $\frac{1}{2} 	imes 5.12 	imes \omega^2 	imes (0.25)^2 = 16$.$2.56 	imes \omega^2 	imes 0.0625 = 16$.$0.16 	imes \omega^2 = 16$.$\omega^2 = \frac{16}{0.16} = 100$.$\omega = 10 \ rad/s$.The time period $T$ is given by $T = \frac{2\pi}{\omega} = \frac{2\pi}{10} = \frac{\pi}{5} \ s$.

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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