Question

A simple pendulum takes $32$ s to complete $20$ oscillations. What is the time period of the pendulum?

Answer 1

Step 1: Given data

The pendulum makes $20$ oscillations in $32$ seconds.

Step 2: Frequency and time period

1. Frequency is defined as the number of complete oscillations in unit time. $Frequency=\frac{Numberofoscillation}{Totaltimetaken}.$
2. The time period of oscillation is the total time for one complete oscillation.
3. The relation between frequency and time period is $f=\frac{1}{T}$, where, f is the frequency and T is the time period of oscillations.

Step 3: Finding the frequency

As we know, $Frequency=\frac{Numberofoscillation}{Totaltimetaken}.$ So,

$$\begin{gathered} f=\frac{20}{32}=0.63 \\ orf=0.63Hz. \end{gathered}$$

Step 4: Finding the time period

We know, the time period, $T=\frac{1}{f}$

So, $$\begin{gathered} T=\frac{1}{f}=\frac{1}{0.63} \\ orT=1.6seconds. \end{gathered}$$

Therefore, the time period of the pendulum is $1.6seconds.$