Question

For a particle executing SHM with an amplitude ‘r’, the kinetic energy will be equal to the potential energy when the displacement is equal to-

Answer 1

x = A sin w t displacement in SHM

v = A w cos w t velocity in SHM

PE = 1/2 k x^2 = 1/2 k A^2 sin^2 w t

KE = 1/2 m v^2 = 1/2 m w^2 A^2 cos^2 w t

If KE = PE then

k sin^2 w t = m w^2 cos^2 w t

sin^2 wt / cos^2 w t = tan^2 w t = m w^2 / k

but k / m = w^2

So tan^2 w t = 1 and tan w t = 1 or w t = pi / 4 or theta = 45 deg

Then x = r sin w t = r sin 45 = .707 r