Question

A particle undergoes $SHM$ of period $T$. The time taken to complete $3/8th$ oscillation starting from the mean position 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 to complete $\frac{1}{8}$th oscillation from extreme position is,

$y=\frac{a}{2}=a\cos wt=a\cos \frac{2\pi }{T}t$

$\Rightarrow \cos \frac{\pi }{3}=\cos \frac{2\pi t}{T}$

$\Rightarrow t=\frac{T}{6}$

w.k.t time taken to complete one fourth oscillation is $\frac{T}{4}$

Therefore the time to complete $\frac{3}{8}$th oscillation

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

$=\frac{5T}{12}$