The P.E. of a particle executing SHM at a dis | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) The potential energy $(PE)$ of a particle executing simple harmonic motion $(SHM)$ is defined as the work done against the restoring force to disp

Vedclass · Accepted Answer

$\frac{1}{2}m{\omega ^2}{x^2}$

Vedclass · Answer

(A) The potential energy $(PE)$ of a particle executing simple harmonic motion $(SHM)$ is defined as the work done against the restoring force to displace the particle from its equilibrium position.The restoring force is given by $F = -kx$,where $k$ is the force constant.The potential energy is calculated by integrating the work done: $PE = \int_{0}^{x} F dx = \int_{0}^{x} kx dx = \frac{1}{2}kx^2$.We know that the angular frequency $\omega$ is related to the force constant $k$ and mass $m$ by the relation $\omega^2 = \frac{k}{m}$,which implies $k = m\omega^2$.Substituting this value of $k$ into the expression for potential energy,we get:$PE = \frac{1}{2}m\omega^2x^2$.

The $P.E.$ of a particle executing $SHM$ at a distance $x$ from its equilibrium position is

Similar Questions

$A$ linear harmonic oscillator has a total mechanical energy of $300 \ J$. If its potential energy at the mean position is $100 \ J$,find its kinetic energy at $x = +\frac{A}{\sqrt{2}}$. (in $J$)

In simple harmonic motion,the total mechanical energy of a given system is $E$. If the mass of the oscillating particle $P$ is doubled,then the new energy of the system for the same amplitude is

$A$ particle starts from the mean position and performs $S.H.M.$ with a period of $4 \ s$. At what time is its kinetic energy $50 \%$ of its total energy (in $s$)?

$A$ body is performing $S.H.M.$ of amplitude $A$. The displacement of the body from a point where kinetic energy is maximum to a point where potential energy is maximum,is

The potential energy of a simple harmonic oscillator at the mean position is $2\,J$. If its mean kinetic energy $(K.E.)$ is $4\,J$,its total energy will be .... $J$

Vedclass Test Series

Exam Paper Generator

Online Exam Module