Question

A loaded vertical spring executes S.H.M. with a time period of 4 sec. The difference between the kinetic

Answer 1

P.E + K.E is constant and P.E and K.E vary like squares of sine and cosine.

So The difference of sin2(x)−cos2(x) has a period of π (period can be seen as 0 at −pi/4 to 3pi/4  ) which is half of period of sine or cosine.