$A$ 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

Which of the following functions of time represent $(a)$ simple harmonic motion and $(b)$ periodic but not simple harmonic? Give the period for each case.
$(1)$ $\sin \omega t - \cos \omega t$
$(2)$ $\sin^2 \omega t$

Give the relation between periodic time and angular frequency.

If the displacement of a particle executing simple harmonic motion is given by $x = 0.5 \cos (125.6 t)$,then the time period of oscillation of the particle is nearly. (Here $x$ is displacement in metre and $t$ is time in second) (in $s$)

Identify the function which represents a non-periodic motion.

$A$ body oscillates with $SHM$ according to the equation (in $SI$ units):
$x = 5 \cos (2 \pi t + \pi / 4)$
At $t = 1.5 \, s$,calculate the:
$(a)$ displacement
$(b)$ speed
$(c)$ acceleration of the body.