The angular frequency of motion whose equation is $4\frac{d^2y}{dt^2} + 9y = 0$ is ($y =$ displacement and $t =$ time).

Define periodic time and frequency,their units,and the relationship between them.

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

$A$ mass $m = 100 \, g$ is attached at the end of a light spring which oscillates on a frictionless horizontal table with an amplitude equal to $0.16 \, m$ and a time period equal to $2 \, s$. Initially,the mass is released from rest at $t = 0$ and displacement $x = -0.16 \, m$. The expression for the displacement of the mass at any time $t$ is:

$A$ particle of mass $m$ is under the influence of a force $F$ which varies with the displacement $x$ according to the relation $F = -kx + F_0$,where $k$ and $F_0$ are constants. The particle,when disturbed,will oscillate:

Fill in the blanks:
$1.$ In $SHM$,......... quantities are always positive.
$2.$ $A$ periodic motion that obeys the force law ......... is only a simple harmonic motion.
$3.$ $A$ $SHO$ with a periodic time of $2 \ s$ starts its oscillation from the lower end of its path of motion; its phase will be .......... at time $t = 2 \ s$.