Velocity and Acceleration in Simple Harmonic Motion

Graph between velocity and displacement of a particle, executing S.H.M. is

Graph between velocity and displacement of a particle, executing S.H.M. is

Particle performing $\mathrm{S}.\mathrm{H}.\mathrm{M}.$ starts from extreme position. Plot a graph of displacement, velocity and acceleration against time.

Particle performing $\mathrm{S}.\mathrm{H}.\mathrm{M}.$ starts from mean position. Plot a graph of displacement, velocity and acceleration against time.

A body describes $\mathrm{S}.\mathrm{H}.\mathrm{M}.$ in a path $0.12\mathrm{m}$ long. Its velocity at the centre of the line is $0.12\mathrm{m}/\mathrm{s}.$ Find the period, and magnitude of velocity at a distance $\sqrt{3}\times {10}^{-2}\mathrm{m}$ from the central position.

A particle executes $\mathrm{S}.\mathrm{H}.\mathrm{M}.$ with amplitude of $10\mathrm{cm}$ and period of $10\mathrm{s}.$ Find the $\left(\mathrm{i}\right)$ velocity, $\left(\mathrm{ii}\right)$ acceleration of the particle at a distance $5\mathrm{cm}$ from the equilibrium position.

A particle is executing $\mathrm{S}.\mathrm{H}.\mathrm{M}.$ of amplitude $5\mathrm{cm}$ and period of  $2\mathrm{s}.$ Find the speed of the particle at a point where its acceleration is half of its maximum value.

The piston in the cylinder head of a locomotive has a stroke of $6\mathrm{ }\mathrm{m}$. If the piston is executing simple harmonic motion with an angular frequency of $200\mathrm{ }\mathrm{r}\mathrm{a}\mathrm{d}\mathrm{ }\mathrm{m}{\mathrm{i}\mathrm{n}}^{-1},$ then maximum speed of the piston is

The average acceleration of a particle performing SHM over one complete oscillation is

The average acceleration of a particle performing $\mathrm{SHM}$(simple harmonic motion) over one complete oscillation is

In SHM match the following.
 

Displacement-time graph of a particle executing SHM is as shown. The corresponding force time graph of the particle can be

A body describes simple harmonic motion with an amplitude of $5 \mathrm{cm}$ and a period of $0.2 \mathrm{s}.$ Find the acceleration and velocity of the body when the displacement is $5 \mathrm{cm}$

A particle executing simple harmonic motion has amplitude of 1 metre and time period 2 second. At t = 0 net force on the particle is zero, find maximum velocity and maximum acceleration

The $x-t$ graph of a particle undergoing simple harmonic motion is shown below. The acceleration of the particle at $t=\frac{4}{3}\mathrm{s}$ is

A point mass oscillates along the  $\text{x}$-axis according to the law $x=x_0 cos\left(\omega t-\pi /4\right)$. If the acceleration of the particle is written as $a=Acos\left(\omega t+\delta \right)$, then