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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 data

The pendulum makes 10 oscillations in 20 seconds.

Step 2: Frequency and time period

  1. Frequency is defined as the number of complete oscillations in unit time. Frequency=NumberofoscillationTotaltimetaken.
  2. The time period of oscillation is the total time for one complete oscillation.
  3. The relation between frequency and time period is f=1T, where, f is the frequency and T is the time period of oscillations.

Step 3: Finding the frequency

As we know, Frequency=NumberofoscillationTotaltimetaken. So,

f=1020=0.5orf=0.5Hz.

Step 4: Finding the time period

We know, the time period, T=1f

So, T=1f=10.5orT=2seconds.

Therefore, the frequency of the pendulum is 0.5Hz and the time period is 2seconds.


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