The ratio between kinetic and potential energ | vedclass

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

Question

(D) Let the amplitude of the simple harmonic motion be $a$. The displacement of the body from the mean position is $x = \frac{a}{N}$.The kinetic energ

Vedclass · Accepted Answer

$N^2-1$

Vedclass · Answer

(D) Let the amplitude of the simple harmonic motion be $a$. The displacement of the body from the mean position is $x = \frac{a}{N}$.The kinetic energy $(KE)$ of the body is given by:$KE = \frac{1}{2} m \omega^2 (a^2 - x^2) = \frac{1}{2} m \omega^2 \left(a^2 - \frac{a^2}{N^2}\right) = \frac{1}{2} m \omega^2 a^2 \left(1 - \frac{1}{N^2}\right) = \frac{1}{2} m \omega^2 a^2 \left(\frac{N^2 - 1}{N^2}\right) \quad (i)$The potential energy $(PE)$ of the body is given by:$PE = \frac{1}{2} m \omega^2 x^2 = \frac{1}{2} m \omega^2 \left(\frac{a}{N}\right)^2 = \frac{1}{2} m \omega^2 \frac{a^2}{N^2} \quad (ii)$Taking the ratio of $KE$ to $PE$:$\frac{KE}{PE} = \frac{\frac{1}{2} m \omega^2 a^2 \left(\frac{N^2 - 1}{N^2}\right)}{\frac{1}{2} m \omega^2 \frac{a^2}{N^2}} = \frac{N^2 - 1}{1} = N^2 - 1$

The ratio between kinetic and potential energies of a body executing simple harmonic motion, when it is at a distance of $\frac{1}{N}$ of its amplitude from the mean position is

Similar Questions

For what value of displacement the kinetic energy and potential energy of a simple harmonic oscillation become equal?

$A$ particle performs $S.H.M.$ of amplitude $A$ with angular frequency $\omega$ along a straight line. When it is at a distance $\frac{\sqrt{3}}{2}A$ from the mean position,its kinetic energy is increased by an amount $\frac{1}{2}m\omega^2A^2$ due to an impulsive force. What is its new amplitude?

The $K.E.$ and $P.E.$ of a particle executing $SHM$ with amplitude $A$ will be equal when its displacement is

$A$ bob of a simple pendulum of mass $m$ performs $SHM$ with amplitude $A$ and period $T$. The kinetic energy of the pendulum at displacement $x = \frac{A}{2}$ will be:

Consider a simple harmonic motion $(SHM)$. Let $K$ and $U$ be kinetic energy and potential energy when the displacement in $SHM$ is one-half $\left(\frac{1}{2}\right)$ the amplitude. Which of the following statements is correct?

Vedclass Test Series

Exam Paper Generator

Online Exam Module