Question

# A simple pendulum makes $10$ oscillations in $20$ seconds. What is the time period and frequency of its oscillation?

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Solution

## Step 1: Given dataThe pendulum makes $10$ oscillations in $20$ 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, $f=\frac{10}{20}=0.5\phantom{\rule{0ex}{0ex}}orf=0.5Hz.$Step 4: Finding the time periodWe know, the time period, $T=\frac{1}{f}$So, $T=\frac{1}{f}=\frac{1}{0.5}\phantom{\rule{0ex}{0ex}}orT=2seconds.$Therefore, the frequency of the pendulum is $0.5Hz$ and the time period is $2seconds.$

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