Write the expression of kinetic energy and potential energy of $SHM$ particle $(i)$ as a function of displacement $(ii)$ as a function of time.

Vedclass pdf generator app on play store
Vedclass iOS app on app store
(N/A) For a particle of mass $m$ performing $SHM$ with angular frequency $\omega$ and amplitude $A$:
$(i)$ As a function of displacement $x$:
Potential Energy $(U)$: $U = \frac{1}{2} m \omega^2 x^2$
Kinetic Energy $(K)$: $K = \frac{1}{2} m \omega^2 (A^2 - x^2)$
$(ii)$ As a function of time $t$ (assuming $x = A \sin(\omega t + \phi)$):
Potential Energy $(U)$: $U = \frac{1}{2} m \omega^2 A^2 \sin^2(\omega t + \phi)$
Kinetic Energy $(K)$: $K = \frac{1}{2} m \omega^2 A^2 \cos^2(\omega t + \phi)$

Explore More

Similar Questions

$A$ simple pendulum of mass $m$ executes $S.H.M.$ with total energy $E$. If at an instant it is at one of the extreme positions,then its linear momentum after a phase shift of $\frac{\pi}{3} \, rad$ will be

In a simple harmonic oscillator,at the mean position:

The displacement of a particle of mass $2 \,g$ executing $SHM$ is given by $y=5 \sin \left(4 t+\frac{\pi}{3}\right)$. Here,$y$ is in metres and $t$ is in seconds. The kinetic energy of the particle,when $t=\frac{T}{4}$ is (in $\,J$)

$A$ particle is executing simple harmonic motion with a time period of $3 \,s$. At a position where the displacement of the particle is $60 \%$ of its amplitude, the ratio of the kinetic and potential energies of the particle is

Position of a $3 \ kg$ mass moving along the $X$-axis is given by $x = 0.3 \cos (\omega t) \ m$. If $K(t)$ denotes the kinetic energy at time $t$,then the value of $\frac{K\left(\frac{\pi}{6 \omega}\right)}{K\left(\frac{\pi}{3 \omega}\right)}$ is

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial
For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free
For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo