For a SHM PE = \(\frac{1}{2}\) kx2
= \(\frac{1}{2}\) mω2 x2 = \(\frac{1}{2}\)mω A2 sin2 ωt
KE= \(\frac{1}{2}\) mv2
v =\(\frac{dx}{dt}\) = – Aω cos ωt
⇒ KE = \(\frac{1}{2}\) mA2ω2 cos2 ωt
Total energy = KE + PE = \(\frac{1}{2}\)mω2 A2 cos2 ωt + \(\frac{1}{2}\)mω2 sin2 ωt
Total energy = \(\frac{1}{2}\) mω2 A2.
