A particle of mass m is executing simple harm | vedclass

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

Question

(C) The total energy $(E)$ of a particle executing simple harmonic motion is given by the sum of its potential energy and kinetic energy.The formula f

Vedclass · Accepted Answer

$\frac{2 \pi^{2} m A^{2}}{T^{2}}$

Vedclass · Answer

(C) The total energy $(E)$ of a particle executing simple harmonic motion is given by the sum of its potential energy and kinetic energy.The formula for total energy is $E = \frac{1}{2} k A^{2}$,where $k$ is the force constant.We know that the angular frequency $\omega = \frac{2 \pi}{T}$.Also,the force constant $k = m \omega^{2}$.Substituting the value of $\omega$ into the expression for $k$,we get $k = m \left( \frac{2 \pi}{T} \right)^{2} = \frac{4 \pi^{2} m}{T^{2}}$.Now,substitute $k$ into the total energy formula: $E = \frac{1}{2} \left( \frac{4 \pi^{2} m}{T^{2}} \right) A^{2}$.Simplifying this,we get $E = \frac{2 \pi^{2} m A^{2}}{T^{2}}$.

$A$ particle of mass $m$ is executing simple harmonic motion about its mean position. If $A$ is the amplitude and $T$ is the period of $S$.$H$.$M$.,then the total energy of the particle is

Similar Questions

Starting from the mean position,a body oscillates simple harmonically with a period $T$. After what time will its kinetic energy be $75 \%$ of the total energy? $(\sin 30^{\circ} = 0.5)$

The total energy of a simple harmonic oscillator is proportional to

The ratio of kinetic energy to the potential energy of a particle executing $SHM$ at a distance equal to half its amplitude,the distance being measured from its equilibrium position,is:

The kinetic energy of $SHM$ is $1/n$ times its potential energy. If the amplitude of the $SHM$ is $A$,what is the displacement of the particle?

In simple harmonic motion,the total mechanical energy of a given system is $E$. If the mass of the oscillating particle $P$ is doubled,then the new energy of the system for the same amplitude is

Vedclass Test Series

Exam Paper Generator

Online Exam Module