For a particle executing simple harmonic motion, what is the...

The acceleration of a particle executing simple harmonic motion is given by $a = -A\omega^2 \sin(\omega t + \phi)$.

The average acceleration over one complete time period $T$ is calculated as the integral of acceleration over the time period divided by $T$.

$\langle a \rangle = \dfrac{1}{T} \int_{0}^{T} -A\omega^2 \sin(\omega t + \phi) dt$

Since the integral of a sinusoidal function over one complete period is zero, the average acceleration is zero.

Alternatively, average acceleration is defined as the change in velocity divided by the time taken. Over one complete time period, the particle returns to its initial state, meaning its initial and final velocities are equal. Therefore, the change in velocity is zero, resulting in an average acceleration of zero.