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Measurement of Time and Motion - A simple pendulum

Grade 7CBSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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A simple pendulum consists of a small metallic ball or a stone, called a bob, suspended from a rigid stand by a thread.

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The motion of a simple pendulum is an example of periodic or oscillatory motion.

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The pendulum is said to have completed one oscillation when its bob, starting from its mean position OO, moves to AA, to BB and back to OO. It also completes one oscillation when it moves from one extreme position AA to the other extreme position BB and comes back to AA.

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The time taken by the pendulum to complete one oscillation is called its time period.

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In the 16th16^{th} century, Galileo Galilei discovered that the time period of a given pendulum is constant for a fixed length, regardless of the displacement (for small amplitudes).

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The basic unit of time is second (symbol ss). Larger units of time are minutes (minmin) and hours (hh).

📐Formulae

Time Period (T)=Total time takenTotal number of oscillationsTime\ Period\ (T) = \frac{\text{Total time taken}}{\text{Total number of oscillations}}

Frequency (f)=Total number of oscillationsTotal time taken=1T\text{Frequency}\ (f) = \frac{\text{Total number of oscillations}}{\text{Total time taken}} = \frac{1}{T}

💡Examples

Problem 1:

A simple pendulum takes 32 s32\ s to complete 2020 oscillations. What is the time period of the pendulum?

Solution:

Total time taken=32 s\text{Total time taken} = 32\ s Number of oscillations=20\text{Number of oscillations} = 20 Time Period=3220=1.6 s\text{Time Period} = \frac{32}{20} = 1.6\ s

Explanation:

To find the time period, we divide the total time recorded by the number of oscillations completed. The resulting value 1.6 s1.6\ s is the time taken for one single oscillation.

Problem 2:

If a pendulum completes 4040 oscillations in 11 minute, calculate its time period.

Solution:

Total time taken=1 min=60 s\text{Total time taken} = 1\ min = 60\ s Number of oscillations=40\text{Number of oscillations} = 40 Time Period(T)=6040=1.5 s\text{Time Period} (T) = \frac{60}{40} = 1.5\ s

Explanation:

First, we must convert the time from minutes to seconds (1 min=60 s1\ min = 60\ s). Then, applying the formula for time period, we divide 6060 by 4040 to get 1.5 s1.5\ s per oscillation.