Physics - SHM Question with Solution | TestHub

The average acceleration of a particle over a given time interval is defined as the total change in velocity divided by the total time taken.

${\vec{a}}_{avg}=\frac{\Delta \vec{v}}{\Delta t}=\frac{{\vec{v}}_f-{\vec{v}}_i}{\Delta t}$

For a particle performing Simple Harmonic Motion (S.H.M.), the velocity is a periodic function of time. After any integer number of complete oscillations, the particle returns to its exact initial state, meaning its final velocity ${\vec{v}}_f$ is equal to its initial velocity ${\vec{v}}_i$.

Over two complete oscillations, the change in velocity is:

$\Delta \vec{v}={\vec{v}}_f-{\vec{v}}_i=0$

Therefore, the average acceleration over two complete oscillations is zero.

Alternatively, the acceleration in S.H.M. is given by $a=-A{\omega }^2\sin (\omega t+\varphi )$. The average value of a sine function over any complete number of cycles is zero.

Answer: zero