At what position in simple harmonic motion ar | vedclass

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

Question

(C) The kinetic energy $(K)$ of a particle in simple harmonic motion is given by $K = \frac{1}{2}m\omega^2(a^2 - y^2)$.The potential energy $(U)$ is g

Vedclass · Accepted Answer

$a/\sqrt{2}$

Vedclass · Answer

(C) The kinetic energy $(K)$ of a particle in simple harmonic motion is given by $K = \frac{1}{2}m\omega^2(a^2 - y^2)$.The potential energy $(U)$ is given by $U = \frac{1}{2}m\omega^2y^2$.Given that the kinetic energy equals the potential energy $(K = U)$:$\frac{1}{2}m\omega^2(a^2 - y^2) = \frac{1}{2}m\omega^2y^2$Canceling the common terms $\frac{1}{2}m\omega^2$ from both sides:$a^2 - y^2 = y^2$$a^2 = 2y^2$$y^2 = \frac{a^2}{2}$$y = \pm \frac{a}{\sqrt{2}}$Therefore,the kinetic and potential energies are equal at the position $y = a/\sqrt{2}$.

At what position in simple harmonic motion are the kinetic energy and potential energy equal?

Similar Questions

$A$ particle is performing $S.H.M.$ with energy of vibration $90 \,J$ and amplitude $6 \,cm$. When the particle reaches a distance of $4 \,cm$ from the mean position,it is stopped for a moment and then released. The new energy of vibration will be ........... $J$.

$A$ particle starting from mean position executes simple harmonic motion with a period $8 \ s$. The minimum time in which its potential energy becomes half of the total energy is . . . . . . . (in $s$)

$A$ 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

$A$ 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

$A$ particle of mass $10 \ g$ performs simple harmonic motion with an amplitude of $10 \ cm$ and a time period of $2 \ s$. What is its kinetic energy at a displacement of $5 \ cm$?

Vedclass Test Series

Exam Paper Generator

Online Exam Module