Q. The periodic time of a body executing simple harmonic motion is $3\ s.$ After how much interval from time $t = 0,$ its displacement will be half of its amplitude
A) $\frac{1}{8}s$
B) $\frac{1}{6}s$
C) $\frac{1}{4}s$
D) $\frac{1}{3}s$
Explanation
(c) $y = a\sin{\frac{2\pi}{T}t \Rightarrow \frac{a}{2} = a\sin{\frac{2\pi t}{3} \Rightarrow \frac{1}{2} = \sin\frac{2\pi t}{3}}}$
$\Rightarrow \sin{\frac{2\pi t}{3} = \sin{\frac{\pi}{6} \Rightarrow \frac{2\pi t}{3} = \frac{\pi}{6} \Rightarrow t = \frac{1}{4}\sec}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.