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

There is a body having mass $m$ and performing $SHM$ with amplitude '$a$'. There is a restoring force $F = -Kx$, where $x$ is the displacement. The total energy of the body depends upon which of the following?

$A$ body performs $S.H.M.$ Its kinetic energy $K$ varies with time $t$ as indicated by which graph?

$A$ linear harmonic oscillator of force constant $2 \times 10^6 \, N/m$ and amplitude $0.01 \, m$ has a total mechanical energy of $160 \, J$. Its

The maximum restoring force of a body executing $SHM$ is $\alpha$ and the total energy is $\beta$. Obtain its amplitude in terms of $\beta$ and $\alpha$.

For any $S.H.M.$,the amplitude is $6\, cm$. If the instantaneous potential energy is half the total energy,then the distance of the particle from its mean position is .... $cm$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module