A particle undergoing simple harmonic motion has time dependent displacement given by x(t)=A (π t)/(90) . The ratio of kinetic to potential energy of this particle at t=210 ~s will be

Correct answer: D. (1)/(3) Kinetic energy, k=(1)/(2) ~m ω^ 2 ~A^ 2 ^ 2 ω t Potential energy, U=(1)/(2) m ω^ 2 A^ 2 ^ 2 ω t (k)/(U)= ^ 2 ω t= ^ 2 (π)/(90)(210)=(1)/(3)

JEE Main 201911 JanuaryMorning Shift

Exam: JEE Main
Year: 2019
Date: 11 January
Shift: Morning Shift
Subject: Physics
Chapter: Oscillations

JEE Main 2019 · 11 January · Morning Shift · Physics · Oscillations

A particle undergoing simple harmonic motion has time dependent...

A particle undergoing simple harmonic motion has time dependent displacement given by

x(t)=\mathrm{A} \sin \frac{\pi t}{90}

. The ratio of kinetic to potential energy of this particle at

\mathrm{t}=210 \mathrm{~s}

will be

Options

A $\frac{1}{9}$
B1
C2
D $\frac{1}{3}$

Correct answer

D. $\frac{1}{3}$

Step-by-step solution

Kinetic energy,

\mathrm{k}=\frac{1}{2} \mathrm{~m} \omega^{2} \mathrm{~A}^{2} \cos ^{2} \omega \mathrm{t}

Potential energy,

U=\frac{1}{2} m \omega^{2} A^{2} \sin ^{2} \omega t

\frac{k}{U}=\cot ^{2} \omega t=\cot ^{2} \frac{\pi}{90}(210)=\frac{1}{3}

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