When a particle executing SHM oscillates with | vedclass

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

Question

$(B)$ The displacement of a particle executing $SHM$ is given by $y = a \sin(\omega t)$.The velocity of the particle is $u = \frac{dy}{dt} = a\omega \

Vedclass · Accepted Answer

changes periodically with a frequency of $2v$

Vedclass · Answer

$(B)$ The displacement of a particle executing $SHM$ is given by $y = a \sin(\omega t)$.The velocity of the particle is $u = \frac{dy}{dt} = a\omega \cos(\omega t)$.The kinetic energy $K$ is given by $K = \frac{1}{2}mu^2 = \frac{1}{2}m(a\omega \cos(\omega t))^2 = \frac{1}{2}m\omega^2 a^2 \cos^2(\omega t)$.Using the trigonometric identity $\cos^2(	heta) = \frac{1 + \cos(2	heta)}{2}$, we get $K = \frac{1}{4}m\omega^2 a^2 (1 + \cos(2\omega t))$.Since the frequency of the $SHM$ is $v = \frac{\omega}{2\pi}$, the frequency of the kinetic energy oscillation is determined by the term $\cos(2\omega t)$, which is $v' = \frac{2\omega}{2\pi} = 2v$.Therefore, the kinetic energy changes periodically with a frequency of $2v$.

When a particle executing $SHM$ oscillates with a frequency $v$, then the kinetic energy of the particle

Similar Questions

The potential energy of a simple harmonic oscillator at the mean position is $2\,J$. If its mean kinetic energy $(K.E.)$ is $4\,J$,its total energy will be .... $J$

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

The kinetic energy of a particle executing simple harmonic motion at a displacement of $3 \ cm$ from the mean position is $4 \ mJ$. If the amplitude of the particle is $5 \ cm$,then the maximum force acting on the particle is (in $N$)

The displacement of a particle of mass $2 \,g$ executing $SHM$ is given by $y=5 \sin \left(4 t+\frac{\pi}{3}\right)$. Here,$y$ is in metres and $t$ is in seconds. The kinetic energy of the particle,when $t=\frac{T}{4}$ is (in $\,J$)

$A$ body is executing a linear $S.H.M.$ Its potential energies at the displacements $x$ and $y$ are $E_1$ and $E_2$ respectively. Its potential energy at displacement $(x+y)$ will be

Vedclass Test Series

Exam Paper Generator

Online Exam Module