The kinetic energy of SHM is 1/n times its po | vedclass

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

Question

(C) The kinetic energy $K$ and potential energy $U$ of a particle in $SHM$ at displacement $x$ are given by:$K = \frac{1}{2} m \omega^{2} (A^{2} - x^{

Vedclass · Accepted Answer

$\sqrt{\frac{n}{n+1}} A$

Vedclass · Answer

(C) The kinetic energy $K$ and potential energy $U$ of a particle in $SHM$ at displacement $x$ are given by:$K = \frac{1}{2} m \omega^{2} (A^{2} - x^{2})$$U = \frac{1}{2} m \omega^{2} x^{2}$Given that $K = \frac{1}{n} U$,we substitute the expressions:$\frac{1}{2} m \omega^{2} (A^{2} - x^{2}) = \frac{1}{n} \left( \frac{1}{2} m \omega^{2} x^{2} \right)$$A^{2} - x^{2} = \frac{x^{2}}{n}$$A^{2} = x^{2} + \frac{x^{2}}{n} = x^{2} \left( 1 + \frac{1}{n} \right) = x^{2} \left( \frac{n+1}{n} \right)$$x^{2} = A^{2} \left( \frac{n}{n+1} \right)$$x = \sqrt{\frac{n}{n+1}} A$

The kinetic energy of $SHM$ is $1/n$ times its potential energy. If the amplitude of the $SHM$ is $A$,then what is the displacement of the particle?

Similar Questions

Which air pollutant is responsible for the Bhopal gas tragedy?

$\int_0^{\pi / 2} \sin ^8 x \cos ^2 x \, dx$ is equal to

Data Entry - Physics

Two numbers are chosen at random from $\{1, 2, 3, 4, 5, 6, 7, 8\}$ at a time. The probability that the smaller of the two numbers is less than $4$ is

The colour sequence in a carbon resistor is red,brown,orange and silver. The resistance of the resistor is

Vedclass Test Series

Exam Paper Generator

Online Exam Module