A particle undergoing simple harmonic motion has time dependent displacement given by $$xt=Asin$$$$π$$$$t90$$. The ratio of kinetic to potential energy of this particle at time $$t=30s$$ will be

Question

A particle undergoing simple harmonic motion has time dependent displacement given by  $$xt=Asin$$$$π$$$$t90$$. The ratio of kinetic to potential energy of this particle at time  $$t=30s$$ will be

Infinity Learn · Accepted Answer

let displacement equation of an oscillator be $$y=Asin$$ωt, here ω is angular velocity,A is Amplitude differentiate y with respect to time t, to get velocity $$v=dydt=A($$$$cos$$ω$$t)$$ω $$KE$$$$=12mv2$$ $$PE$$$$=12m$$ω$$2y2$$     Substitute displacement and velocity in $$PE$$,$$KE$$ and take ratio, $$KEPE=12m$$ω$$2A2cos2$$ω$$t12m$$ω$$2A2sin2$$ωt $$KEPE=cot2$$ωt, by the question $$w=$$π$$90$$ at time  t $$=$$ $$30$$ ⇒ KEPE $$=$$ $$cot2$$$$π$$$$90$$×$$30=cot2$$$$π$$$$3=13$$

A particle undergoing simple harmonic motion has time dependent displacement given by $x (t) = A \sin \frac{π t}{90}$ . The ratio of kinetic to potential energy of this particle at time $t = 30 s$ will be

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A particle undergoing simple harmonic motion has time dependent displacement given by xt=Asinπt90. The ratio of kinetic to potential energy of this particle at time t=30s will be

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A particle undergoing simple harmonic motion has time dependent displacement given by $x (t) = A \sin \frac{π t}{90}$ . The ratio of kinetic to potential energy of this particle at time $t = 30 s$ will be