Oscillations Part 1

As we know that, for a body executing SHM the average kinetic energy is equal to average potential energy over a complete time period i.e. $\text{KE}_{\text{av}} = \text{PE}_{\text{av}} = \frac{1}{4} m \omega^{2} a^{2}$ ∴ Total mechanical energy at any time = Sum of kinetic and potential energy $= \frac{1}{2} m \omega^{2} a^{2} =$ constant. where, m = mass of body executing SHM, ω = angular frequency and a = amplitude of SHM. Hence, (c) and (d) are true.