Question

A particle undergoes simple harmonic motion having time-period T. The time taken 3/8th oscillation is-

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

Answer 1

The correct option is C $\frac{5}{12}T$

Time taken to complete one fourth oscillation is $\frac{T}{4}$ // where $T$ is the time period .

So time to complete ${\frac{1}{8}}^{th}$ oscillation from to extreme position is obtained from

$y=a/2=acos\omega t=acos\frac{2\pi }{T}t$

Or, $acos\frac{\pi }{3}=acos\frac{2\pi }{T}t$

Or,$t=\frac{T}{6}$ s .

Hence time to complete 3/8th oscillation

${\frac{1}{8}}^{th}+{\frac{1}{4}}^{th}$

$=\frac{T}{4}+\frac{T}{6}=\frac{5}{12}T$