Energy in Simple Harmonic Motion

A particle of mass $m$ oscillates in Simple Harmonic Motion between points $x_1$ and $x_2$, the equilibrium position being $O$. Which of the following graphs represents the variation of its potential energy $\left(U\right)$ with respect to its position?

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

Which of the given is graph of the square of cosine function?

Draw the function of the square of sine.

Plot the graph of potential energy versus time for simple harmonic motion.

A particle is executing simple harmonic motion with a time period T. At time t = 0, it is at its position of equilibrium. The kinetic energy - time graph of the particle will look like:

For a simple pendulum, a graph is plotted between its kinetic energy ($KE$) and potential energy ($PE$) against its displacement $d$. Which one of the following represents these correctly?
(graphs are schematic and not drawn to scale)

The ratio of kinetic energy at a mean position to potential energy at $\frac{A}{2}$ of a particle performing $\mathrm{SHM}$ is

$U$ is the potential energy of an oscillating(SHM) particle and $F$ is the force acting on it at a given instant. Which of the following is correct?

(Given $x$ is displacement of the particle)

A particle of mass $m$ oscillates with simple harmonic motion between points $x_1$ and $x_2$, the equilibrium position being at $O$. Its potential energy is plotted. It will be as given below in the graph,

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 potential energy of a simple harmonic oscillator of mass $2 \mathrm{kg}$ at its mean position is $5 \mathrm{J}$. If its total energy is $9 \mathrm{J}$ and amplitude is $1 \mathrm{cm}$, then its time period is

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

A simple pendulum of length $L$ has mass $M$ and it oscillates freely with amplitude $A$. At extreme position, its potential energy is ($g$= acceleration due to gravity)

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 $\mathrm{S}.\mathrm{H}.\mathrm{M}.$