Question

A particle undergoes simple harmonic motion having time period $T$. The time taken in $\frac{3}{8}th$ oscillation 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)

$\frac{5}{12}T$

Time to complete $1/4th$ oscillation is $\frac{T}{4}s$. Time to complete $\frac{1}{8}th$ vibration from extreme position is obtained from
$y=\frac{a}{2}=a\cos \omega t=a\cos \frac{2\pi }{T}t$ or $t=\frac{T}{6}s$
So time to complete $3/8th$ oscillation $=\frac{T}{4}+\frac{T}{6}=\frac{5T}{12}$