If equation of displacement of a particle is = A sin PT + B cos PT then motion of particle is

y = A sin PT + B cos PTDifferentiate w.r.t. to T, dydT = PA cos PT – PB sin PTAgain differentiate w.r.t. to T, d2ydT2= – P2A sin PT – BP2 cos PT= – P2 [A sin PT + B cos PT] ⇒+ P2y = 0 This is equation for S.H.M