Energy of a Particle Performing S.H.M

Total energy of a particle of mass $200 \mathrm{g}$ performing linear SHM is ${10}^{-3} \mathrm{J}$. Find its maximum velocity.

The total energy in simple harmonic motion at the mean position is purely potential.

What is the total energy in simple harmonic motion at the mean position ?

In SHM, what will be the kinetic energy value at mean position?

Potential energy at the mean position of SHM is _____.

At the mean position, the total energy in simple harmonic motion is 

A particle executing SHM with an amplitude $\mathrm{A}$. The displacement of the particle when its potential energy is half of its total energy is

The total energy of a particle executing linear S.H.M. is purely potential at both extreme points of its motion.

The total energy of a particle executing linear S.H.M. is purely potential at both extreme points of its motion.

A block of mass $1 \mathrm{kg}$ tied to a long spring of spring constant $100 \mathrm{N} {\mathrm{m}}^{-1}$ is at rest on a horizontal frictionless surface. The block is pulled through a distance $5 \mathrm{cm}$ from its equilibrium position and released. Then the total energy of the block when it is at a distance $4 \mathrm{cm}$ from the equilibrium position is

The $KE$ and $PE$ of a particle executing simple harmonic motion with amplitude $A$ has ratio $2:1$, then its displacement is,

Obtain an expression for potential energy of a particle performing$\mathrm{S}.\mathrm{H}.\mathrm{M}.$ What is the value of potential energy at
(i) mean position
(ii) extreme position?

A particle executes $\mathrm{S}.\mathrm{H}.\mathrm{M}.$with a period $8\mathrm{s}.$ Find the time in which half the total energy is potential.

An object performing $\mathrm{S}.\mathrm{H}.\mathrm{M}.$ with mass  $0.5 \mathrm{kg},$ force constant $10 \mathrm{N}/\mathrm{m}$ and amplitude $3 \mathrm{cm}. \left(\mathrm{a}\right)$ What is the total energy of the object? $\left(\mathrm{b}\right)$ What is its maximum speed? $\left(\mathrm{c}\right)$ What is the speed at $\mathrm{x}=2 \mathrm{cm} ? \left(\mathrm{d}\right)$ What is kinetic and potential energy at $\mathrm{x}=2 \mathrm{cm} ?$

Show that energy of $\mathrm{S}.\mathrm{H}.\mathrm{M}.$ is directly proportional to $\left(\mathrm{i}\right)$ square of amplitude and
$\left(\mathrm{ii}\right)$square of frequency.

When the displacement in $\mathrm{S}.\mathrm{H}.\mathrm{M}.$ is ${\frac{1}{3}}^{\mathrm{rd}}$ of the amplitude. What fraction of total energy is kinetic energy and what fraction is potential energy?

Obtain expressions for kinetic energy, potential energy and total energy of a particle performing linear $\mathrm{S}.\mathrm{H}.\mathrm{M}.$

Show that the total energy of the particle performing linear $\mathrm{S}.\mathrm{H}.\mathrm{M}.$ is constant.

A particle undergoing simple harmonic motion has time dependent displacement given by $x\left(t\right)=A\mathrm{s}\mathrm{i}\mathrm{n}\frac{\pi t}{90}$. The ratio of kinetic to potential energy of this particle at $t=210 \mathrm{s}$ will be:

If $x=A\sin \frac{\pi }{90}t$ then find ratio of $K.E$ and $P.E$ at $t=210 \mathrm{s}\mathrm{e}\mathrm{c}$