A child swinging on a swing in sitting position, stands up. Then the time period of swing will:

Concept:

Simple Pendulum

• An ideal simple pendulum consists of a heavy point mass body (bob) suspended by a weightless, inextensible, and perfectly flexible string from rigid support about which it is free to oscillate.
• For a simple pendulum, the time period of swing of a pendulum depends on the length of the string and acceleration due to gravity,

\(\Rightarrow T=2\pi\sqrt{\frac{l}{g}}\,\)

• The above formula is only valid for small angular displacements.

Where, T = Time period of oscillation, l = Effective length of the pendulum, and g = gravitational acceleration

Explanation:

• The swinging girl can be considered as a simple pendulum.

The time period of oscillation of the simple pendulum is,

\(\Rightarrow T=2\pi\sqrt{\frac{l}{g}}\,\)

where l is the effective length of the simple pendulum.

• The length of the simple pendulum is equal to the distance from point of suspension to the centre of gravity (CG) of the oscillating body.
• When the girl stands up, the distance of CG from the point of suspension decreases.
• Therefore, the time period of oscillation also decreases.