Physics, asked by Tanisha1409, 1 year ago

Derive an expression for the total energy of a particle executing simple harmonic motion

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Answered by Rishabh7755
87
Here is the total energy of SHM.
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Answered by nirman95
28

TOTAL ENERGY OF SHM:

  • The total energy of a particle executing simple harmonic motion will be the sum of potential energy and kinetic energy.

Let the amplitude be 'a' , angular frequency be \omega and the mass of the object be 'm':

TE = PE + KE

 \implies TE =  \dfrac{1}{2} m { \omega}^{2}  {x}^{2}  +  \dfrac{1}{2} m { \omega}^{2} ( {a}^{2}  -  {x}^{2} )

 \implies TE =  \dfrac{1}{2} m { \omega}^{2} ( {a}^{2}   +  {x}^{2} -  {x}^{2} )

 \implies TE =  \dfrac{1}{2} m { \omega}^{2}  {a}^{2}

So, total energy of particle is ½ma².

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