Consider a simple harmonic motion (SHM). Let | vedclass

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

Question

(D) The potential energy $U$ of a body performing $SHM$ is given by $U = \frac{1}{2} k x^2$, where $x$ is the displacement from the mean position.Give

Vedclass · Accepted Answer

$\frac{K}{U}=3$

Vedclass · Answer

(D) The potential energy $U$ of a body performing $SHM$ is given by $U = \frac{1}{2} k x^2$, where $x$ is the displacement from the mean position.Given that the displacement $x = \frac{a}{2}$, where $a$ is the amplitude:$U = \frac{1}{2} k \left(\frac{a}{2}\right)^2 = \frac{1}{2} k \frac{a^2}{4} = \frac{1}{8} k a^2$ ... $(i)$The kinetic energy $K$ of the body is given by $K = \frac{1}{2} k (a^2 - x^2)$.Substituting $x = \frac{a}{2}$:$K = \frac{1}{2} k \left(a^2 - \frac{a^2}{4}\right) = \frac{1}{2} k \left(\frac{3 a^2}{4}\right) = \frac{3}{8} k a^2$ ... (ii)Taking the ratio of kinetic energy to potential energy:$\frac{K}{U} = \frac{\frac{3}{8} k a^2}{\frac{1}{8} k a^2} = 3$.

Consider a simple harmonic motion $(SHM)$. Let $K$ and $U$ be kinetic energy and potential energy when the displacement in $SHM$ is one-half $\left(\frac{1}{2}\right)$ the amplitude. Which of the following statements is correct?

Similar Questions

$A$ 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 $\,J$)

The kinetic energy of a particle,executing simple harmonic motion is $16 \ J$ when it is in the mean position. If the amplitude of motion is $25 \ cm$ and the mass of the particle is $5.12 \ kg$,the period of oscillation is

If $T$ is the period of $SHM$,then write the period of kinetic and potential energy.

Vibrational motion possesses which type of energy?

For a particle performing $S.H.M.$,when displacement is $x$,the potential energy and restoring force acting on it are denoted by $E$ and $F$ respectively. The relation between $x, E$ and $F$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module