The kinetic energy and potential energy of a | vedclass

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

Question

(C) Let the displacement of the particle be $y$ and the amplitude be $a$. The potential energy $(U)$ and kinetic energy $(K)$ of a particle in simple

Vedclass · Accepted Answer

$\frac{a}{\sqrt{2}}$

Vedclass · Answer

(C) Let the displacement of the particle be $y$ and the amplitude be $a$. The potential energy $(U)$ and kinetic energy $(K)$ of a particle in simple harmonic motion are given by:$U = \frac{1}{2} m \omega^2 y^2$$K = \frac{1}{2} m \omega^2 (a^2 - y^2)$According to the problem,$U = K$:$\frac{1}{2} m \omega^2 y^2 = \frac{1}{2} m \omega^2 (a^2 - y^2)$$y^2 = a^2 - y^2$$2y^2 = a^2$$y^2 = \frac{a^2}{2}$$y = \frac{a}{\sqrt{2}}$

The kinetic energy and potential energy of a particle executing simple harmonic motion will be equal,when displacement (amplitude = $a$) is

Similar Questions

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

The kinetic energy of $SHM$ is $1/n$ times its potential energy. If the amplitude of the $SHM$ is $A$,what is the displacement of the particle?

The total energy of a particle executing $SHM$ at an amplitude of $4 \, cm$ is $20 \, J$. What will be its total energy at a displacement of $x = 2 \, cm$ (in $J$)?

The displacement between the position of maximum potential energy and the position of maximum kinetic energy for a particle executing $S.H.M.$ is

At which point (place) does a particle executing $SHM$ have maximum kinetic energy and maximum potential energy?

Vedclass Test Series

Exam Paper Generator

Online Exam Module