Question

A particle undergoes simple harmonic motion having time period T. The time taken in 3/8^th oscillations is

• A. $\frac{3}{8}T$
• B. $\frac{5}{8}T$
• C. $\frac{5}{12}T$
• D. $\frac{7}{12}T$

Answer 1

Answer: (C)

$\frac{5}{12}T$

Answer 2

Time to complete $\frac{1}{4}$th of the oscillations of $\frac{T}{4}$s.

Time to complete $\frac{1}{8}$th vibration means when the vibrating particle reaches from the extreme position to the half the amplitude

⇒ y = $\frac{A}{2}$ = A sin$\left( \omega t + \frac{\pi}{2} \right)$ = A cosωt ⇒ t = $\frac{T}{6}$s

∴ Total time required $\frac{T}{6} = \frac{5T}{12}$