$A$ simple harmonic motion is represented by $F(t) = 10\sin(20t + 0.5)$. The amplitude of the $S.H.M.$ is $a = $ ....

The displacement $x$ (in metres) of a particle performing simple harmonic motion is related to time $t$ (in seconds) as $x = 0.05 \cos \left( 4 \pi t + \frac{\pi}{4} \right)$. The frequency of the motion will be ..... $Hz$.

The equation of an $S.H.M.$ with amplitude $A$ and angular frequency $\omega$ in which all distances are measured from one extreme position and time is taken to be zero at the other extreme position is ...

Why is the periodic time $T = \frac{2\pi}{\omega}$ taken for the function $f(t) = A \cos \omega t$?

$A$ particle executes simple harmonic motion with an amplitude '$A$'. The distance travelled by it in one periodic time is

Which of the following examples represent periodic motion?
$(a)$ $A$ swimmer completing one (return) trip from one bank of a river to the other and back.
$(b)$ $A$ freely suspended bar magnet displaced from its $N-S$ direction and released.
$(c)$ $A$ hydrogen molecule rotating about its centre of mass.
$(d)$ An arrow released from a bow.