Question

Calculate time period of a simple pendulum if it takes 72 seconds to complete 24 oscillations

Answer 1

Answer:

The time period of a simple pendulum if it takes 72 seconds to complete 24 oscillation will be 3 seconds.          

Step-by-step explanation:

Total number of oscillations = 24

Time taken to complete 24 oscillations = 2 seconds

So, the frequency 'f' of the simple pendulum will be:

                                                       $f=\frac{24}{72}$

                                                       $f=\frac{1}{3}$

Let 'T' be the time period.

                                           $T=\frac{1}{f}$

                                           $T=\frac{1}{\frac{1}{3}}$

                      $\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{1}{\frac{b}{c}}=\frac{c}{b}$

                                           $T=\frac{3}{1}$

                                           $T=3$

Therefore, the time period of a simple pendulum if it takes 72 seconds to complete 24 oscillation will be 3 seconds.                  

Answer 2

It takes 3 seconds for the pendulum to complete 1 oscillation.

Given to us:

Total number of oscillations = 24 oscillations,

The time period needed for 24 oscillations = 72 seconds,

The time period needed for 1 oscillation,

${\rm Time\ period\ needed\ for\ 1\ Oscillation &=\dfrac{Time\ period\ needed\ for\ 24\ Oscillations}{Total\ number\ of\ oscillations} }$

$\begin{aligned}\\{\rm Time\ period\ needed\ for\ 1\ Oscillation &=\dfrac{72\ seconds}{24\ oscillations}\\\\&=3\ seconds/oscillation \end{aligned}$

Hence, It takes 3 seconds for the pendulum to complete 1 oscillation.

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