Question

Particle performing S.H.M. starts from mean position. Plot a graph of displacement, velocity and acceleration against time.

Answer 1

we know, simple harmonic motion is a sinusoidal wave . equation of S.H.M is given by $x=Asin\omega t$
where x is the displacement of particle , A is the amplitude , $\omega$ is the angular velocity of particle .
graph of $x=Asin\omega t$ as shown in figure.

now differentiate displacement, x with respect to time.
$\frac{dx}{dt}=v=A\omega cos\omega t$
here v denotes velocity of particle performing S.H.M from mean position.
see figure, it shows the graph of velocity.

now ,differentiate velocity with respect to time .
$\frac{dv}{dt}=a=-A\omega^2sin\omega t$ , here a denotes the acceleration of the particle performing S.H.M
see figure, it shows the graph of acceleration.