Physics - SHM Question with Solution | TestHub

The acceleration of a particle in SHM is given by $a(t)=-{\omega }^{2}x(t)$. If $x(t)=A\sin (\omega t+\varphi )$, then $a(t)=-A{\omega }^2\sin (\omega t+\varphi )$. Average acceleration is defined as $⟨a⟩=\frac{\Delta v}{\Delta t}$.

For one complete oscillation, the particle returns to its initial state (same position and same velocity). Therefore, the change in velocity $\Delta v$ over one complete oscillation is zero. Hence, the average acceleration during one complete oscillation is $0$.