Question

Determine whether or not the following quantities can be in the same direction for SHM (a) displacement and velocity (b) velocity and acceleration (c) displacement and acceleration.

Answer 1

We know,

Equation of SHM with zero phase constant,

$y=A\sin \left(\omega t\right)$ (displacement)

$v=\frac{dy}{dt}=A\Omega \sin \left(\omega t\right)$ (velocity)

$a=\frac{dv}{dt}=-A{\omega }^2\sin \left(\omega t\right)$ (acceleration)

$\text{It is clear that displacement and velocity are in same direction,}$

And velocity and acceleration aren't in same direction as well as displacement and acceleration aren't in same direction.