For a particle executing simple harmonic moti | vedclass

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

Question

(A) The potential energy $(U)$ of a particle in simple harmonic motion at displacement $x$ is given by $U = \frac{1}{2} k x^2$,where $k$ is the force

Vedclass · Accepted Answer

$3: 1$

Vedclass · Answer

(A) The potential energy $(U)$ of a particle in simple harmonic motion at displacement $x$ is given by $U = \frac{1}{2} k x^2$,where $k$ is the force constant.Given that the displacement $x = \frac{A}{2}$,where $A$ is the amplitude,the potential energy is $U = \frac{1}{2} k (\frac{A}{2})^2 = \frac{1}{8} k A^2$.The total energy $(E)$ of the particle is $E = \frac{1}{2} k A^2$.The kinetic energy $(K)$ is given by $K = E - U = \frac{1}{2} k A^2 - \frac{1}{8} k A^2 = \frac{3}{8} k A^2$.The ratio of kinetic energy to potential energy is $\frac{K}{U} = \frac{\frac{3}{8} k A^2}{\frac{1}{8} k A^2} = \frac{3}{1}$.Thus,the ratio is $3: 1$.

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

Similar Questions

$A$ particle of mass $10 \ g$ performs simple harmonic motion with an amplitude of $10 \ cm$ and a time period of $2 \ s$. What is its kinetic energy at a displacement of $5 \ cm$?

$A$ particle starts from the mean position and performs $S.H.M.$ with a period of $4 \ s$. At what time is its kinetic energy $50 \%$ of its total energy (in $s$)?

Show that for a particle in linear $SHM$,the average kinetic energy over a period of oscillation equals the average potential energy over the same period.

The total energy of a particle executing $S.H.M.$ is $80 \, J$. What is the potential energy when the particle is at a distance of $\frac{3}{4}$ of amplitude from the mean position?

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 $\,J$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module