Write equation of SHM for a situation with angular frequency $\omega$ and amplitude $A,$ if the particle is situated at $\frac{A}{\sqrt{2}}$ at $t=0$ and is going towards mean position.

Two particles $P$ and $Q$ are executing SHM across same straight line whose equations are given by $y_P=A\sin \left(\omega t+{\varphi }_1\right)$ and $y_Q=A\sin \left(\omega t+{\varphi }_2\right).$ An observer, at $t=0,$ observes the particle $\text{'}P\text{'}$ at distance $\frac{A}{2}$ moving to the right from mean position $O$ while $Q$ at $\frac{-\sqrt{3}}{2}A$ moving to the left from mean position $O$ as shown.

Find $\left({\varphi }_2-{\varphi }_1\right).$

A particle slides back and forth between two inclined frictionless planes.

If $h$ is the initial height of the particle, the period of oscillation _________.

A particle slides back and forth between two inclined frictionless planes.

Is the motion oscillatory? Is it SHM?

The equation of motion of a particle started at $t=0$ is given by $x=5\sin \left(20t+\frac{\pi }{3}\right)$ where $x$ is in centimetres and $t$ is in second. When does the particle

first come to rest __________.

The equation of motion of a particle started at $t=0$ is given by $x=5\sin \left(20t+\frac{\pi }{3}\right)$ where $x$ is in centimetres and $t$ is in second. When does the particle

first have zero acceleration __________.

The equation of motion of a particle started at $t=0$ is given by $x=5\sin \left(20t+\frac{\pi }{3}\right)$ where $x$ is in centimetres and $t$ is in second. When does the particle

first have maximum speed __________.