If $x=5 \sin \left(\pi t+\frac{\pi}{3}\right) \text{ m}$ represents the motion of a particle executing simple harmonic motion,the amplitude and time period of motion,respectively,are

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.

Two particles are executing Simple Harmonic Motion ($S$.$H$.$M$.). The equations of their motion are $y_1 = 10 \sin \left( \omega t + \frac{\pi}{4} \right)$ and $y_2 = 25 \sin \left( \omega t + \frac{\sqrt{3} \pi}{4} \right)$. What is the ratio of their amplitudes?

$A$ function is represented by the equation $y = A \cos \omega t \cos 2\omega t + A \sin \omega t \sin 2\omega t$. Then the nature of the function is:

$Assertion :$ In simple harmonic motion,the motion is to and fro and periodic.
$Reason :$ Velocity of the particle $(v) = \omega \sqrt {A^2 - x^2}$ (where $x$ is the displacement and $A$ is the amplitude).

The motion of the particle is given by the equation $x = A \sin \omega t + B \cos \omega t$. The motion of the particle is: