Average velocity of a particle executing $SHM$ in one complete vibration is

What is the value of frequency in the differential equation of $SHM$ $\frac{d^{2}x}{dt^{2}} + 100x = 0$?

Equations $y_1 = A \sin \omega t$ and $y_2 = \frac{A}{2} \sin \omega t + \frac{A}{2} \cos \omega t$ represent $S.H.M.$ The ratio of the amplitudes of the two motions is

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):
$(a)$ $\sin \omega t - \cos \omega t$
$(b)$ $\sin^3 \omega t$
$(c)$ $3 \cos (\pi/4 - 2 \omega t)$
$(d)$ $\cos \omega t + \cos 3 \omega t + \cos 5 \omega t$
$(e)$ $\exp(-\omega^2 t^2)$
$(f)$ $1 + \omega t + \omega^2 t^2$

The figure depicts four $x-t$ plots for the linear motion of a particle. Which of the plots represent periodic motion? What is the period of motion (in case of periodic motion)?

$A$ system exhibiting $S.H.M.$ must possess