$A$ simple harmonic motion having an amplitude $A$ and time period $T$ is represented by the equation: $y = 5 \sin \pi (t + 4) \ m$. Then the values of $A$ (in $m$) and $T$ (in $sec$) are:

If displacement $x$ and velocity $v$ are related as $4v^2 = 25 - x^2$ in a $SHM$. Then the time period of the given $SHM$ is (Consider $SI$ units).

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

The equation of $SHM$ of a particle is given as $2 \frac{d^2x}{dt^2} + 32x = 0$,where $x$ is the displacement from the mean position of rest. The period of its oscillation (in seconds) is

Write the difference between oscillation and vibrations.

Write the force law for $SHM$ and obtain the formula for the period of an $SHM$ particle.