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

For a particle executing simple harmonic motion,the kinetic energy $K$ is given by $K = K_0 \cos^2 \omega t$. The maximum value of potential energy is

As a body performs $S.H.M.$,its potential energy $U$ varies with time $t$ as indicated in:

$A$ 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?

$A$ body is executing simple harmonic motion. At a displacement $x$,its potential energy is $E_1$ and at a displacement $y$,its potential energy is $E_2$. The potential energy $E$ at a displacement $(x+y)$ is

$A$ particle of mass $4 \,kg$ is executing $SHM$. Its displacement is given by the equation $y=8 \cos [100 t+\pi / 4] \,cm$. Its maximum kinetic energy is (in $\,J$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module