What is the amplitude of a particle executing uniform circular motion?

In simple harmonic motion,the acceleration of a particle is given by $a = -bx$. What is the time period of the motion?

If a $SHM$ is represented by $\frac{d^2x}{dt^2} + ax = 0$,its time period is:

Give the relation between periodic time and angular frequency.

Which of the following functions of time represent $(a)$ simple harmonic,$(b)$ periodic but not simple harmonic,and $(c)$ non-periodic motion? Give period for each case of periodic motion ($\omega$ is any positive constant):
$(a)$ $\sin \omega t - \cos \omega t$
$(b)$ $\sin^3 \omega t$
$(c)$ $3 \cos (\pi/4 - 2 \omega t)$
$(d)$ $\cos \omega t + \cos 3 \omega t + \cos 5 \omega t$
$(e)$ $\exp(-\omega^2 t^2)$
$(f)$ $1 + \omega t + \omega^2 t^2$

$A$ particle performs $SHM$ with a period $T$ and amplitude $a.$ The mean velocity of the particle over the time interval during which it travels a distance $a/2$ from the extreme position is