Assertion (A) In S.H.M kinetic and potential energy become equal when the distance is 1 / 2 times its amplitude. Reason (R) The potential energy of a particle executing S.H.M is periodic with time period being maximum at the extreme displacement.

Step-by-step solution

( In SHM, K. E of oscillator = 1 2 m ^2 (a^2-y^2 ) P. E of oscillator = 1 2 m ^2 y^2 (Here, a= amplitude and y= displacement) when, K . E = P . E aligned & 1 2 m ^2 (a^2-y^2 ) & = 1 2 m ^2 y^2 & a^2 & =2 y^2 or & y & = a 2 aligned And P. E is maximum when y=a or particle is at extreme displacement position. Hence, reason (R) is correct but it does not explain (A).