A particle starts its oscillation from the eq | vedclass

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

Question

(B) The displacement of a particle starting from the equilibrium position is given by $x = A \sin(\omega t)$.Given $t = \frac{T}{6}$ and $\omega = \fr

Vedclass · Accepted Answer

$1:3$

Vedclass · Answer

(B) The displacement of a particle starting from the equilibrium position is given by $x = A \sin(\omega t)$.Given $t = \frac{T}{6}$ and $\omega = \frac{2\pi}{T}$,we have $x = A \sin(\frac{2\pi}{T} \cdot \frac{T}{6}) = A \sin(\frac{\pi}{3}) = A \frac{\sqrt{3}}{2}$.The kinetic energy $(KE)$ is given by $KE = \frac{1}{2}k(A^2 - x^2) = \frac{1}{2}k(A^2 - \frac{3A^2}{4}) = \frac{1}{2}k(\frac{A^2}{4})$.The potential energy $(PE)$ is given by $PE = \frac{1}{2}kx^2 = \frac{1}{2}k(\frac{3A^2}{4})$.Therefore,the ratio $\frac{KE}{PE} = \frac{\frac{1}{2}k(A^2/4)}{\frac{1}{2}k(3A^2/4)} = \frac{1}{3}$.

$A$ particle starts its oscillation from the equilibrium position with time period $T$. Find the ratio of kinetic energy to potential energy of the particle at time $t = \frac{T}{6}$.

Similar Questions

For a particle executing $S.H.M.$, the potential energy is $n$ times the kinetic energy when its displacement from mean position is $(\frac{2\sqrt{2}}{3})A$, where $A$ is the amplitude of $S.H.M.$ The value of $n$ is

The kinetic energy and potential energy of a particle executing simple harmonic motion will be equal,when displacement (amplitude = $a$) is

$A$ particle is executing simple harmonic motion $(SHM)$ of amplitude $A$ along the $x$-axis about $x = 0$. When its potential energy $(PE)$ equals kinetic energy $(KE)$,the position of the particle will be

$A$ particle is executing linear simple harmonic motion of amplitude $A$. At what displacement is the energy of the particle half potential and half kinetic?

For a particle performing $S.H.M.$,when displacement is $x$,the potential energy and restoring force acting on it are denoted by $E$ and $F$ respectively. The relation between $x, E$ and $F$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module