JEE Main · 2021 · 31 Aug 2021 · Shift 2 · Elasticity & SHM

In simple harmonic motion the kinetic and potential energies depend on position and are equal only at $x=\pm A/\sqrt{2}$, so the claim that the potential energy always equals the kinetic energy is false. Their averages coincide only over a whole period, not over an arbitrary interval, so the claim that the average potential and kinetic energies over any interval are equal is false. The total energy $\frac{1}{2}m{\omega }^2{A}^2$ is conserved at every instant, so the sum of the kinetic and potential energy is constant. Averaged over one full period the kinetic and potential energies are each $\frac{1}{4}m{\omega }^2{A}^2$ and hence equal. The true statements are that the sum of the kinetic and potential energy is constant and that the period-averaged kinetic and potential energies are equal.