Question

What is the phase difference between acceleration and velocity of a particle executing simple harmonic motion?

Answer 1

We know that,

The velocity is

$v=A\omega \cos (\omega t+\varphi )$

The acceleration is

$a=-A{\omega }^2\sin (\omega t+\varphi )$

Now,

$\cos (\omega t+\varphi +\frac{\pi }{2})=-\sin (\omega t+\varphi )$

Now, the acceleration is

$a=A{\omega }^2\cos (\omega t+\varphi +\frac{\pi }{2})$

Hence, the phase difference is $\frac{\pi }{2}$