If the displacement $(x)$ and velocity $(v)$ of a particle executing simple harmonic motion are related through the expression $4v^2 = 25 - x^2$, then the time period is

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

The displacement of an oscillator is given by $x = a \sin \omega t + b \cos \omega t$,where $a, b$ and $\omega$ are constants. Then:

The figure shows the circular motion of a particle. The radius of the circle is $B$,the period is $30 \ s$,the sense of revolution is clockwise,and the initial position at $t = 0$ is at an angle of $45^\circ$ (or $\pi/4$ radians) with the positive $y$-axis in the first quadrant. The simple harmonic motion of the $x$-projection of the radius vector of the rotating particle $P$ is:

The displacement of a particle is given at time $t$,by: $x = A \sin (-2 \omega t) + B \sin^2 \omega t$. Then,

If the displacement equation of a particle is represented by $y = A\sin PT + B\cos PT$,the particle executes