Question

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

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Solution

Step 1: Given dataThe pendulum makes $20$ oscillations in $32$ seconds.Step 2: Frequency and time periodFrequency is defined as the number of complete oscillations in unit time. $Frequency=\frac{Numberofoscillation}{Totaltimetaken}.$The time period of oscillation is the total time for one complete oscillation.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 frequencyAs we know, $Frequency=\frac{Numberofoscillation}{Totaltimetaken}.$ So, $f=\frac{20}{32}=0.63\phantom{\rule{0ex}{0ex}}orf=0.63Hz.$Step 4: Finding the time periodWe know, the time period, $T=\frac{1}{f}$So, $T=\frac{1}{f}=\frac{1}{0.63}\phantom{\rule{0ex}{0ex}}orT=1.6seconds.$Therefore, the time period of the pendulum is $1.6seconds.$

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