Q. A body is executing S.H.M. When its displacement from the mean position is $4\ cm$ and $5\ cm,$ the corresponding velocity of the body is $10\ cm/s$ and $8\ cm/s.$ Then the time period of the body is
A) $2\pi\ s$
B) $\pi/2\ s$
C) $\pi\ s$
D) $3\pi/2s$
Explanation
(c) $v = \omega\sqrt{a^{2} - y^{2}} \Rightarrow 10 = \omega\sqrt{a^{2} - (4)^{2}}\ $and$\ 8 = \omega\sqrt{a^{2} - (5)^{2}}$
On solving $\omega = 2 \Rightarrow \omega = \frac{2\pi}{T} = 2 \Rightarrow T = \pi s$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.