Two equations of two $S.H.M.$ are $y = a\sin(\omega t - \alpha)$ and $y = b\cos(\omega t - \alpha)$. The phase difference between the two is .... $^\circ$.

The displacement of a particle from its mean position (in metre) is given by
$y = 0.2 \sin (10 \pi t + 1.5 \pi) \cos (10 \pi t + 1.5 \pi)$
The motion of the particle is

$A$ ball is released from height $h$ which makes a perfectly elastic collision with the ground. The frequency of the periodic vibratory motion is ($g$ = acceleration due to gravity).

Plot the corresponding reference circle for each of the following simple harmonic motions. Indicate the initial $(t = 0)$ position of the particle,the radius of the circle,and the angular speed of the rotating particle. For simplicity,the sense of rotation may be fixed to be anticlockwise in every case: ($x$ is in $cm$ and $t$ is in $s$).
$(a)\; x = -2 \sin (3t + \pi/3)$
$(b)\; x = \cos (\pi/6 - t)$
$(c)\; x = 3 \sin (2\pi t + \pi/4)$
$(d)\; x = 2 \cos \pi t$

What is displacement? Explain its general meaning by giving examples.

Equations $y = 2A \cos^2 \omega t$ and $y = A (\sin \omega t + \sqrt{3} \cos \omega t)$ represent the motion of two particles.