Time period of a simple pendulum is T . If its length increases by 2 %, the new time period beco

step 1 Hello students in this question we have a simple pendulum simple pendulum having time period of

Time period of a simple pendulum is T . If its length...

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Key Concepts

Simple Pendulum

A simple pendulum consists of a weight suspended from a fixed point so that it can swing freely. Its motion can be approximated as simple harmonic motion, provided the oscillation angles are small.

Time Period Formula

The time period of a simple pendulum is given by T = 2??(L/g), where L is the length of the pendulum and g is the acceleration due to gravity. This formula reflects how the time period depends on the square root of the pendulum's length.

Dependence on Length

Since the time period T is proportional to the square root of the length (T ? ?L), any change in the length of the pendulum results in a change in the period by the square root of the factor by which the length changes.

Binomial Approximation for Small Changes

For small percentage changes in length, the square root function can be approximated using the binomial expansion. For example, an increase of 2% in length gives ?(1.02) ? 1 + 0.01, which means the period increases by approximately 1%.

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