Let the SHM equation be
x = Asin ω t
Potential energy is given by
= \(\frac{1}{2}\) kx2 = \(\frac{1}{2}\) m ω2 k2
= \(\frac{1}{2}\) mω2 A2 sin2 ω t
Kinetic energy = \(\frac{1}{2}\) mv2
= \(\frac{1}{2}\) m ω2 A2 cos2 ω t
Total energy = PE + KE
= \(\frac{1}{2}\) mω2 A2 sin2 ω t + \(\frac{1}{2}\) mω2 A2 cos2 ω t
= \(\frac{1}{2}\) mω2 A2.
