A particle undergoing simple harmonic motion | vedclass

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

Question

(C) The amplitude of the particle performing $SHM$ is $A = 10 \ cm$.The instantaneous displacement of the particle is $x = 6 \ cm$.The kinetic energy

Vedclass · Accepted Answer

$16: 9$

Vedclass · Answer

(C) The amplitude of the particle performing $SHM$ is $A = 10 \ cm$.The instantaneous displacement of the particle is $x = 6 \ cm$.The kinetic energy $(K)$ of the particle is given by $K = \frac{1}{2} m \omega^2 (A^2 - x^2)$.The potential energy $(U)$ of the particle is given by $U = \frac{1}{2} m \omega^2 x^2$.The ratio of kinetic energy to potential energy is $\frac{K}{U} = \frac{\frac{1}{2} m \omega^2 (A^2 - x^2)}{\frac{1}{2} m \omega^2 x^2} = \frac{A^2 - x^2}{x^2}$.Substituting the values,we get $\frac{K}{U} = \frac{10^2 - 6^2}{6^2} = \frac{100 - 36}{36} = \frac{64}{36}$.Simplifying the fraction,$\frac{K}{U} = \frac{16}{9}$.Thus,the ratio of kinetic energy to potential energy is $16: 9$.

$A$ particle undergoing simple harmonic motion has an amplitude of $10 \ cm$. When the particle is at a displacement of $6 \ cm$ from the centre,then the ratio of its kinetic energy to potential energy is

Similar Questions

$A$ linear harmonic oscillator of force constant $2 \times 10^6\,N/m$ and amplitude $0.01\,m$ has a total mechanical energy of $160\,J$. Which of the following statements is correct?

The amplitude of a particle executing $SHM$ is $3\,cm$. The displacement at which its kinetic energy will be $25\%$ more than the potential energy is: $.............cm$.

$A$ body executes simple harmonic motion with an amplitude $A$. At what displacement,from the mean position,is the potential energy of the body one fourth of its total energy?

Amplitude of a $SHO$ is $\sqrt{5} \ cm$. At what displacement from the mean position the ratio of kinetic energy to potential energy is $4$ (in $cm$)?

For the minimum time period condition,find the average potential energy between $t = 0$ to $t = 0.05 \ s$ (take $g = 10 \ m/s^2$).

Vedclass Test Series

Exam Paper Generator

Online Exam Module