A particle is vibrating in a simple harmonic | vedclass

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

Question

(D) The total energy $E$ of a particle in simple harmonic motion is the sum of its kinetic energy $(K.E.)$ and potential energy $(P.E.)$.Given that at

Vedclass · Accepted Answer

$2\sqrt{2}\, cm$

Vedclass · Answer

(D) The total energy $E$ of a particle in simple harmonic motion is the sum of its kinetic energy $(K.E.)$ and potential energy $(P.E.)$.Given that at displacement $x$,the kinetic energy is equal to the potential energy,i.e.,$K.E. = P.E.$We know that $P.E. = \frac{1}{2}m\omega^2x^2$ and $K.E. = \frac{1}{2}m\omega^2(a^2 - x^2)$,where $a$ is the amplitude.Setting $K.E. = P.E.$:$\frac{1}{2}m\omega^2(a^2 - x^2) = \frac{1}{2}m\omega^2x^2$$a^2 - x^2 = x^2$$2x^2 = a^2$$x^2 = \frac{a^2}{2}$$x = \frac{a}{\sqrt{2}}$Given $a = 4\, cm$,we have:$x = \frac{4}{\sqrt{2}} = 2\sqrt{2}\, cm$.Thus,the correct option is $D$.

$A$ particle is vibrating in a simple harmonic motion with an amplitude of $4\, cm$. At what displacement from the equilibrium position is its energy half potential and half kinetic?

Similar Questions

For a particle performing $S.H.M.$,when displacement is $x$,the potential energy and restoring force acting on it are denoted by $E$ and $F$ respectively. The relation between $x, E$ and $F$ is

$A$ particle performs $S.H.M.$ Its potential energies are $U_{1}$ and $U_{2}$ at displacements $x_{1}$ and $x_{2}$ respectively. At displacement $(x_{1} + x_{2})$,its potential energy $U$ is:

$A$ body is executing simple harmonic motion. At a displacement $x$,its potential energy is $E_1$ and at a displacement $y$,its potential energy is $E_2$. The potential energy $E$ at a displacement $(x+y)$ is

$A$ vertical mass-spring system executes simple harmonic oscillations with a period of $2\, s$. $A$ quantity of this system which exhibits simple harmonic variation with a period of $1\, s$ is

Explain and draw the graphs of kinetic energy,potential energy,and mechanical energy versus displacement for $SHM$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module