Study of which motion is required to understand many physical phenomena?

The motion of a particle executing $S.H.M.$ is given by $x = 0.01 \sin 100\pi (t + 0.05)$,where $x$ is in metres and $t$ is in seconds. The time period is ..... $sec$.

$A$ particle executing simple harmonic motion along the $Y$-axis has its motion described by the equation $y = A \sin(\omega t) + B$. The amplitude of the simple harmonic motion is

One end of a rod of length $L$ is fixed to a point on the circumference of a wheel of radius $R$. The other end is sliding freely along a straight channel passing through the centre of the wheel as shown in the figure below. The wheel is rotating with a constant angular velocity $\omega$ about $O$. Taking $T = \frac{2 \pi}{\omega}$,the motion of the rod is

Write the difference between oscillations and vibrations.

$A$ particle executes simple harmonic motion and is located at $x = a, b$ and $c$ at times $t_0, 2t_0$ and $3t_0$ respectively. The frequency of the oscillation is