In a simple harmonic oscillation,what fractio | vedclass

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

Question

(C) The total mechanical energy $E$ of a particle in simple harmonic motion is given by $E = \frac{1}{2} m \omega^{2} A^{2}$.At any position $x$,the k

Vedclass · Accepted Answer

$3/4$

Vedclass · Answer

(C) The total mechanical energy $E$ of a particle in simple harmonic motion is given by $E = \frac{1}{2} m \omega^{2} A^{2}$.At any position $x$,the kinetic energy $K$ is given by $K = \frac{1}{2} m \omega^{2} (A^{2} - x^{2})$.The particle is midway between the mean position $(x = 0)$ and the extreme position $(x = A)$,so $x = \frac{A}{2}$.Substituting $x = \frac{A}{2}$ 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 $K = \frac{3}{4} E$.Thus,the fraction of total mechanical energy in the form of kinetic energy is $3/4$.

In a simple harmonic oscillation,what fraction of total mechanical energy is in the form of kinetic energy,when the particle is midway between mean and extreme position?

Similar Questions

For a particle executing $S.H.M.$,its potential energy is $8$ times its kinetic energy at a certain displacement $x$ from the mean position. If $A$ is the amplitude of $S.H.M.$,the value of $x$ is:

For a particle executing simple harmonic motion,the kinetic energy of the particle at a distance of $4 \,cm$ from the mean position is $\frac{1}{3}$ of the maximum kinetic energy. The amplitude of the motion 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?

The potential energy of a simple harmonic oscillator when the particle is half way to its end point is (where $E$ is the 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