Question

A particle undergoes SHM of period T starting from mean position. The time taken in ${\frac{3}{8}}^{th}$ oscillation is

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

The time to complete ${\frac{3}{8}}^{th}$ oscillation = time to complete ${\frac{1}{4}}^{th}$ oscillation + time to complete ${\frac{1}{8}}^{th}$ oscillation from the extreme. The time to complete ${\frac{1}{4}}^{th}$ oscillation = $\frac{T}{4}$
The time taken to complete ${\frac{1}{8}}^{th}$ oscillation from extreme position is obtained from the equation,
$y=\frac{a}{2}=a\cos \omega t$ $\therefore \cos \omega t=\frac{1}{2}\Rightarrow \cos \frac{2\pi }{T}t=\frac{1}{2}$
$t=\frac{T}{6}s\therefore$ The total time $=\frac{T}{4}+\frac{T}{6}=\frac{5T}{12}$