In a simple harmonic motion,when the displace | vedclass

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

Question

(B) The total energy $(E)$ of a particle in simple harmonic motion is given by $E = \frac{1}{2} m \omega^2 a^2$,where $a$ is the amplitude.The kinetic

Vedclass · Accepted Answer

$3/4$

Vedclass · Answer

(B) The total energy $(E)$ of a particle in simple harmonic motion is given by $E = \frac{1}{2} m \omega^2 a^2$,where $a$ is the amplitude.The kinetic energy $(K)$ at any displacement $(x)$ is given by $K = \frac{1}{2} m \omega^2 (a^2 - x^2)$.Given that the displacement $x = \frac{a}{2}$,we substitute this into the kinetic energy formula:$K = \frac{1}{2} m \omega^2 (a^2 - (\frac{a}{2})^2)$$K = \frac{1}{2} m \omega^2 (a^2 - \frac{a^2}{4})$$K = \frac{1}{2} m \omega^2 (\frac{3a^2}{4})$$K = \frac{3}{4} (\frac{1}{2} m \omega^2 a^2)$Since $E = \frac{1}{2} m \omega^2 a^2$,we have $K = \frac{3}{4} E$.Therefore,the fraction of the total energy that is kinetic is $3/4$.

In a simple harmonic motion,when the displacement is one-half the amplitude,what fraction of the total energy is kinetic?

Similar Questions

$A$ particle starts from the mean position and performs $S.H.M.$ with a period of $4 \ s$. At what time is its kinetic energy $50 \%$ of its total energy (in $s$)?

$A$ 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 of mass $10 \, g$ is describing $S.H.M.$ along a straight line with a period of $2 \, s$ and an amplitude of $10 \, cm$. Its kinetic energy when it is at $5 \, cm$ from its equilibrium position is

$A$ particle is executing $SHM$ with an amplitude $A$. What is the displacement of the particle when its potential energy is half of its total energy?

For a simple pendulum,a graph is plotted between its kinetic energy $(KE)$ and potential energy $(PE)$ against its displacement $d.$ Which one of the following represents these correctly? (graphs are schematic and not drawn to scale)

Vedclass Test Series

Exam Paper Generator

Online Exam Module