The potential energy of a simple harmonic osc | vedclass

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

Question

(A) Given: Total energy $E = 9 \,J$, Potential energy at mean position $U_{mean} = 5 \,J$, Mass $m = 2 \,kg$, Amplitude $A = 1 \,cm = 10^{-2} \,m$. Th

Vedclass · Accepted Answer

$\frac{\pi}{100} \,s$

Vedclass · Answer

(A) Given: Total energy $E = 9 \,J$, Potential energy at mean position $U_{mean} = 5 \,J$, Mass $m = 2 \,kg$, Amplitude $A = 1 \,cm = 10^{-2} \,m$. The total energy of an $SHM$ is the sum of kinetic and potential energy. At the mean position, the potential energy is $U_{mean} = 5 \,J$. Therefore, the maximum kinetic energy $K_{max}$ at the mean position is $K_{max} = E - U_{mean} = 9 \,J - 5 \,J = 4 \,J$. In $SHM$, the maximum kinetic energy is equal to the maximum potential energy at the extreme position, which is given by $\frac{1}{2} k A^2$. So, $\frac{1}{2} k A^2 = 4 \,J$. Substituting $A = 10^{-2} \,m$: $\frac{1}{2} k (10^{-2})^2 = 4 \implies \frac{1}{2} k (10^{-4}) = 4 \implies k = 8 	imes 10^4 \,N/m$. The time period $T$ is given by $T = 2 \pi \sqrt{\frac{m}{k}}$. Substituting the values: $T = 2 \pi \sqrt{\frac{2}{8 	imes 10^4}} = 2 \pi \sqrt{\frac{1}{4 	imes 10^4}} = 2 \pi 	imes \frac{1}{2 	imes 10^2} = \frac{\pi}{100} \,s$.

The potential energy of a simple harmonic oscillator of mass $2 \,kg$ at its mean position is $5 \,J$. If its total energy is $9 \,J$ and amplitude is $1 \,cm$, then its time period is

Similar Questions

When a longitudinal wave propagates through a medium,the particles of the medium execute simple harmonic oscillations about their mean positions. These oscillations of a particle are characterised by an invariant

$A$ particle oscillates along the $x$-axis according to the law,$x(t) = x_0 \sin^2\left(\frac{t}{2}\right)$,where $x_0 = 1 \text{ m}$. The kinetic energy $(K)$ of the particle as a function of $x$ is correctly represented by the graph.

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

The average kinetic energy in one time period of a $SHM$ is :-

$U$ is the potential energy $(PE)$ of an oscillating particle and $F$ is the force acting on it at a given instant. Which of the following is true?

Vedclass Test Series

Exam Paper Generator

Online Exam Module