The mean kinetic energy of a particle executing SHM over one full oscillation, given mass of particle $$=$$ m, amplitude $$=$$ A, angular frequency $$=$$ω $$)$$.

Question

The mean kinetic energy of a particle executing SHM over one full oscillation, given  mass of particle $$=$$ m, amplitude $$=$$ A, angular frequency $$=$$ω  $$)$$.

Infinity Learn · Accepted Answer

for a simple harmonic oscillator, $$displacement=x=Asin$$ωt  differentiate with respect to time t, to obtain velocity, $$velocity=v=A$$ω$$cos$$ωt $$KE$$$$=12mv2$$ $$KE$$$$=12mA$$ω$$cos$$ω$$t2$$ $$KE$$$$=12m$$ω$$2A2cos2$$ωt Mean of a $$function==$$∫$$0Tf(t)dt$$∫$$0Tdt$$ $$KEmean=$$∫$$0T($$$$KE$$$$)dt$$∫$$0Tdt$$ $$KEmean=$$∫$$0T12m$$ω$$2A2cos2$$ωtdtT $$KEmean=12m$$ω$$2A2T$$∫$$0Tcos2$$ωtdt $$KEmean=12m$$ω$$2A2T$$∫$$0T1+cos2$$ω$$t2dt$$ $$KEmean=12m$$ω$$2A2Tt2+sin2$$ω$$t4$$ω$$0T$$ $$KEmean=12m$$ω$$2A2TT2$$ $$KEmean=14m$$ω$$2A2=mean$$ kinetic energy of a particle executing SHM over one full oscillation

The mean kinetic energy of a particle executing SHM over one full oscillation, given mass of particle = m, amplitude = A, angular frequency = $ω$ ).

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The mean kinetic energy of a particle executing SHM over one full oscillation, given mass of particle = m, amplitude = A, angular frequency =ω ).

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The mean kinetic energy of a particle executing SHM over one full oscillation, given mass of particle = m, amplitude = A, angular frequency = $ω$ ).