Question

The periodic time of a body executing S.H.M. is 2 sec. after how much interval from t = 0., will its displacement be half of its amplitude?

Answer 1

Here, T = 2s; t = ?, y = a/2

Now, y = asin ωt = asin\(\frac{2\pi}{T}t\) (∵ T = 2s)

∴  \(\frac{a}{2}=asin\frac{2\pi}{T}t=asin\,\pi t\)

Or  sin πt = \(\frac{1}{2}\)

∴ sin 30º = sin \(\frac{\pi}{6}\) 

Or πt = \(\frac{\pi}{6}\)  or t = \(\frac{1}{6}\)sec.