A body performs linear simple harmonic motion | vedclass

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

Question

(B) The total energy $(E)$ of a body in simple harmonic motion is given by $E = \frac{1}{2} kA^2$,where $k$ is the force constant and $A$ is the ampli

Vedclass · Accepted Answer

$\frac{A}{2}$

Vedclass · Answer

(B) The total energy $(E)$ of a body in simple harmonic motion is given by $E = \frac{1}{2} kA^2$,where $k$ is the force constant and $A$ is the amplitude.The potential energy $(U)$ at a displacement $x$ from the mean position is given by $U = \frac{1}{2} kx^2$.According to the problem,the potential energy is one-fourth of the total energy:$U = \frac{1}{4} E$Substituting the expressions for $U$ and $E$:$\frac{1}{2} kx^2 = \frac{1}{4} (\frac{1}{2} kA^2)$Canceling $\frac{1}{2} k$ from both sides:$x^2 = \frac{A^2}{4}$Taking the square root of both sides:$x = \pm \frac{A}{2}$Thus,at a displacement of $\frac{A}{2}$ from the mean position,the potential energy is one-fourth of the total energy.

$A$ body performs linear simple harmonic motion of amplitude $A$. At what displacement from the mean position is the potential energy of the body one-fourth of its total energy?

Similar Questions

$A$ particle is vibrating in a simple harmonic motion with an amplitude of $4\, cm$. At what displacement from the equilibrium position is its energy half potential and half kinetic?

$A$ particle of mass $m$ oscillates with simple harmonic motion between points $X_1$ and $X_2$,the equilibrium position being $O$. Its potential energy will be as shown in the following graph:

$A$ body is performing $S.H.M.$ of amplitude $A$. The displacement of the body from a point where kinetic energy is maximum to a point where potential energy is maximum,is

Write the maximum velocity of a $SHM$ oscillator in terms of mechanical energy $E$ and mass of oscillator $m$.

Find the displacement of a simple harmonic oscillator at which its $PE$ is half of the maximum energy of the oscillator.

Vedclass Test Series

Exam Paper Generator

Online Exam Module