Q: A particle of mass 1 kg is executing SHM with an amplitude of 1 m and time period π s. Calculate kinetic energy of the particle at the moment when the displacement is 0.8 m.

Sol: $\large \omega = \frac{2\pi}{T} = \frac{2\pi}{\pi} = 2 sec $

$\large v = \omega \sqrt{a^2 – x^2}$

$\large v = 2 \sqrt{1^2 – (0.8)^2}$

v = 2 × 0.6 = 1.2 m/s

Kinetic energy $\large = \frac{1}{2}m v^2 = \frac{1}{2} \times 1 \times (1.2)^2$

K.E = 0.72 J