Q. A particle doing simple harmonic motion, amplitude $= 4\ cm,$ time period $= 12\ s.$ The ratio between time taken by it in going from its mean position to $2\ cm$ and from $2\ cm$ to extreme position is
A) 1
B) 1/3
C) 1/4
D) 1/2
Explanation
(d) $\omega = \frac{2\pi}{T} = \frac{2\pi}{12} = \frac{\pi}{6}\ \frac{rad\ }{\sec}\ (For\ y = 2\ cm)\ 2 = 4\left( \sin\frac{\pi}{6}t_{1} \right)$
By solving $t_{1} = 1sec$ $(For\ y = 4\ cm)\ t_{2} = 3\ sec$
So time taken by particle in going from $2\ cm$ to extreme position is $t_{2} - t_{1} = 2\ sec.$ Hence required ratio will be $\frac{1}{2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.