A simple pendulum of mass m executes S.H.M. w | vedclass

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

Question

(B) The total energy of a simple harmonic oscillator is $E = \frac{1}{2} k A^2$,where $A$ is the amplitude.At the extreme position,the phase $\phi = 0

Vedclass · Accepted Answer

$\sqrt{\frac{3 m E}{2}}$

Vedclass · Answer

(B) The total energy of a simple harmonic oscillator is $E = \frac{1}{2} k A^2$,where $A$ is the amplitude.At the extreme position,the phase $\phi = 0$ (or $\pi$). Let the displacement be $x = A \cos(\omega t)$.After a phase shift of $	heta = \frac{\pi}{3}$,the displacement becomes $x = A \cos(\frac{\pi}{3}) = \frac{A}{2}$.The potential energy at this position is $U = \frac{1}{2} k x^2 = \frac{1}{2} k (\frac{A}{2})^2 = \frac{1}{4} (\frac{1}{2} k A^2) = \frac{E}{4}$.The kinetic energy $K$ at this position is $K = E - U = E - \frac{E}{4} = \frac{3E}{4}$.Since kinetic energy $K = \frac{p^2}{2m}$,we have $\frac{p^2}{2m} = \frac{3E}{4}$.Solving for momentum $p$,we get $p^2 = \frac{6mE}{4} = \frac{3mE}{2}$.Therefore,$p = \sqrt{\frac{3mE}{2}}$.

$A$ simple pendulum of mass $m$ executes $S.H.M.$ with total energy $E$. If at an instant it is at one of the extreme positions,then its linear momentum after a phase shift of $\frac{\pi}{3} \, rad$ will be

Similar Questions

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 $\alpha$.

The variation of displacement with time of a particle executing free simple harmonic motion is shown in the figure. The potential energy $U(x)$ versus time $t$ plot of the particle is correctly shown in figure:

For a particle executing simple harmonic motion,the ratio of kinetic and potential energies at a point where displacement is one half of the amplitude is

The maximum potential energy of a block executing $S.H.M.$ is $E$ and amplitude of oscillation is $A$. The kinetic energy of the block at amplitude $A/2$ is

Starting from the origin,a body oscillates simple harmonically with a time period of $2 \ s$. After what time will its kinetic energy be $75 \%$ of the total energy?

Vedclass Test Series

Exam Paper Generator

Online Exam Module