A particle executes simple harmonic motion with time period $$4$$ second. If it starts its motion from extreme position, then the time interval after which its kinetic energy will be equal to its potential energy for the first time is

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Infinity Learn · Accepted Answer

Equation of SHM is $$x=Acos$$ωt∴ Kinetic energy, $$K=12mV2=12mA2$$ω$$2sin2$$ωtPotential energy, $$U=12m$$ω$$2x2=12m$$ω$$2A2cos2$$ωtWhen K $$=$$ U, we get $$sin2$$ω$$t=cos2$$ωt⇒$$tan$$ω$$t=$$±$$1$$∴ ω$$t=$$π$$4$$,$$3$$$$π$$$$4$$,$$5$$$$π$$$$4$$,$$7$$$$π$$$$4$$,........etc.∴ $$2$$$$π$$$$Ttmin=$$π$$4$$⇒$$tmin=T8=48S=0.5$$ S

A particle executes simple harmonic motion with time period 4 second. If it starts its motion from extreme position, then the time interval after which its kinetic energy will be equal to its potential energy for the first time is

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