Question

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

• A. $\frac{\pi}{5}$sec
• B. $2\pi$sec
• C. $20\pi$sec
• D. $5\pi$sec

Answer 1

Answer: (A)

$\frac{\pi}{5}$sec

Answer 2

At mean position, the kinetic energy is maximum.

Hence $\frac{1}{2}ma^{2}\omega^{2} = 16$

On putting the values we get $\omega = 10\mspace{6mu} \Rightarrow \mspace{6mu} T = \frac{2\pi}{\omega} = \frac{\pi}{5}\sec$