As a body performs S.H.M.,its potential energ | vedclass

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

Question

(B) The potential energy $U$ of a particle performing $S.H.M.$ is given by $U = \frac{1}{2} k x^2$,where $x = A \sin(\omega t + \phi)$.Substituting $x

Vedclass · Accepted Answer

Vedclass · Answer

(B) The potential energy $U$ of a particle performing $S.H.M.$ is given by $U = \frac{1}{2} k x^2$,where $x = A \sin(\omega t + \phi)$.Substituting $x$,we get $U = \frac{1}{2} k A^2 \sin^2(\omega t + \phi) = \frac{1}{4} k A^2 (1 - \cos(2\omega t + 2\phi))$.This expression shows that $U$ is always non-negative $(U \ge 0)$ and varies sinusoidally with a frequency double that of the displacement $(2\omega)$.Looking at the options,graph $B$ represents a function that is always non-negative and has a frequency double that of the standard sine wave,starting from zero at $t=0$ (assuming $\phi = 0$).Therefore,graph $B$ correctly represents the variation of potential energy with time.

As a body performs $S.H.M.$,its potential energy $U$ varies with time $t$ as indicated in:

Similar Questions

Starting from the origin,a particle oscillates simple harmonically with a time period of $2 \ s$. After what time will its kinetic energy be $75 \%$ of the total energy?

$A$ body performs simple harmonic oscillations along the straight line $ABCDE$ with $C$ as the midpoint of $AE.$ Its kinetic energies at $B$ and $D$ are each one-fourth of its maximum value. If $AE = 2R,$ the distance between $B$ and $D$ is

The $K.E.$ and $P.E.$ of a particle executing $SHM$ with amplitude $A$ will be equal when its displacement is

Draw plots of mechanical energy,potential energy,and kinetic energy versus displacement for different positions of a block attached to a spring.

An object of mass $0.2 \,kg$ executes simple harmonic motion along the $x$-axis with a frequency of $(\frac{25}{\pi}) \,Hz$. At the position $x=0.04 \,m$, the object has a kinetic energy of $0.5 \,J$ and a potential energy of $0.4 \,J$. The amplitude of oscillation is ............ $cm$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module