Show that for a particle executing simple harmonic motion the average value of kinetic energy is equal to the average value of potential energy.

Show that for a particle executing simple harmonic motion the average

1.	Show that for a particle executing simple harmonic motion the average value of kinetic energy is equal to the average value of potential energy.
Answer» <html><body><p></p>Solution :Total energy <br/> `T.E=(<a href="https://interviewquestions.tuteehub.com/tag/1-256655" style="font-weight:bold;" target="_blank" title="Click to know more about 1">1</a>)/(2)m <a href="https://interviewquestions.tuteehub.com/tag/omega-585625" style="font-weight:bold;" target="_blank" title="Click to know more about OMEGA">OMEGA</a>^(2)y^(2)+(1)/(2)m omega^(2)(A^(2)-y^(2))` <br/> But`y=a sin omega t` <br/> `T.E. =(1)/(2) m omega^(2)A^(2) sin^(2)omega t+(1)/(2)m omega^(2)A^(2) cos ^(2) omega t` <br/> `=(1)/(2)m omega^(2)A^(2)(sin^(2) omegatt+ cos^(2) omegat)` <br/> From trignometryidentity <br/> `Sin^(2)omegat+cos^(2) omega t=1` <br/> `:. T.E.=(1)/(2)m omega^(2)A^(2)(1)` <br/> `=(1)/(2)m omega^(2)A^(2)` <br/> `:. {:("<a href="https://interviewquestions.tuteehub.com/tag/average-13416" style="font-weight:bold;" target="_blank" title="Click to know more about AVERAGE">AVERAGE</a>"),("potential energy"):}}= {{:("Average"),("Kinetic energy"):}` <br/> `=(1)/(2)` (total energy)</body></html>