Question

Time period of a simple pendulum is $T$. Time taken by it to complete position is $\frac{3}{8}$ oscillations starting from mean position is:

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

Answer 1

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

Time taken to complete one-fourth oscillation is $\frac{T}{4}$ .

So, time taken to complete ${\left(\frac{1}{8}\right)}^{th}$ oscillation from the extreme position is obtained from,

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

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

$t=\left(\frac{T}{6}\right)S$

time to complete ${\left(\frac{1}{3}\right)}^{th}$ oscillation $=\frac{T}{4}+\frac{T}{6}$$=\frac{5T}{12}$

Hence, time to complete ${\left(\frac{1}{3}\right)}^{th}$ oscillation $=\frac{5T}{12}$