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JEE Main 2006
Exam
JEE Main
Year
2006
Subject
Physics
Chapter
Oscillations

JEE Main 2006 · Physics · Oscillations

Starting from the origin, a body oscillates simple harmonically...

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?

Options

  1. A112 s\frac{1}{12} \mathrm{~s}
  2. B16 s\frac{1}{6} \mathrm{~s}
  3. C14 s\frac{1}{4} \mathrm{~s}
  4. D13s\frac{1}{3} s

Correct answer

B. 16 s\frac{1}{6} \mathrm{~s}

Step-by-step solution

\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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