The equation of motion of a particle executing simple harmonic motion is $4 \frac{d^2 y}{dt^2}+\pi^2 y=0$,where $y$ is in metres and $t$ is in seconds. The time period of oscillation of the particle is (in $s$)

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

Which of the following examples represent periodic motion?
$(a)$ $A$ swimmer completing one (return) trip from one bank of a river to the other and back.
$(b)$ $A$ freely suspended bar magnet displaced from its $N-S$ direction and released.
$(c)$ $A$ hydrogen molecule rotating about its centre of mass.
$(d)$ An arrow released from a bow.

$A$ function is represented by the equation $y = A \cos \omega t \cos 2\omega t + A \sin \omega t \sin 2\omega t$. Then the nature of the function is:

Write the difference between oscillations and vibrations.

The displacement of a particle performing $S.H.M.$ is given by $Y = A \cos [\pi(t + \phi)]$. If at $t = 0$,the displacement is $y = 2 \text{ cm}$ and velocity is $v = 2\pi \text{ cm/s}$,the value of amplitude $A$ in $\text{cm}$ is: