Obtain the differential equation of linear simple harmonic motion.

Two equation of two simple harmonic motion are $x=a\sin (\omega t-\alpha ) and y=b\cos (\omega t-\alpha ).$The phase difference between the two is:-

A particle is subjected to two mutually perpendicular simple harmonic motions such that its x and y coordinates are given by $x=2\sin \omega t; y=2\sin (\omega t+\frac{\mathrm{\pi }}{4})$. The path of the particle will be

If a particle is acted by two simple harmonic motions simultaneously, the path of particle is:

Find the resultant amplitude, when two waves of same frequency but with amplitudes $a_1 and a_2$​ superimpose with a phase difference of $\pi /2$will be

Find its speed when it is located at distance of $A/2$ from mean position. A particle is executing SHM with amplitude A and has maximum velocity $V_0$​.

The displacement of a particle is represented by the equation $y=\sin 3\omega t$. The motion is

Find an expression for energy of a body vibrating in SHM.