A particle of mass m is executing simple harm | vedclass

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(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

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

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(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

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