Oscillations

JEE Main level, single correct, medium

100 of 194

Question 100 of 194

Starting from the origin, a body oscillates simple harmonically with a period of 2 s2 \mathrm{~s}. After what time will its kinetic energy be 75%75 \% of the total energy?

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Answer: (B) 16 s\frac{1}{6} \mathrm{~s}

12mv2=34(12mvmax⁡2)\frac{1}{2} m v^2=\frac{3}{4}\left(\frac{1}{2} m v_{\max }^2\right)
A2ω2cos⁡2ωt⇒34 A2ω2\mathrm{A}^2 \omega^2 \cos ^2 \omega \mathrm{t} \Rightarrow \frac{3}{4} \mathrm{~A}^2 \omega^2
cos⁡ωt=32\cos \omega \mathrm{t}=\frac{\sqrt{3}}{2}
ωt=π6⇒t=16\omega t=\frac{\pi}{6} \Rightarrow t=\frac{1}{6} sec

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