The mass of a particle is $1\,kg$ and it is moving along the $x-$axis. The period of its small oscillation is $\frac{\pi}{2}$. Its potential energy may be:

The function $\sin^2(\omega t)$ represents:

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 $s$)

The displacement of a particle varies with time according to the relation $x = a \sin \omega t + b \cos \omega t$.

Which of the following examples represent (nearly) simple harmonic motion and which represent periodic but not simple harmonic motion?
$(a)$ The rotation of Earth about its axis.
$(b)$ Motion of an oscillating mercury column in a $U$-tube.
$(c)$ Motion of a ball bearing inside a smooth curved bowl,when released from a point slightly above the lowermost point.
$(d)$ General vibrations of a polyatomic molecule about its equilibrium position.

What are called normal modes of oscillation of a system?