$A$ particle executing simple harmonic motion of amplitude $5\, cm$ has a maximum speed of $31.4\, cm/s$. The frequency of its oscillation is ..... $Hz$.

For a particle showing motion under the force $F = -5(x - 2)$,the motion is ...........

How many amplitudes does a Simple Harmonic Oscillator $(SHO)$ cover in half of its time period?

The displacement of a particle along the $x$ axis is given by $x = a \sin^2 \omega t$. The motion of the particle corresponds to

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 the difference between periodic motion and simple harmonic motion?