A simple pendulum having bob of mass m and length of string l has time period of T. If the mass of the bob is doubled and the length of the string is halved, then the time period of this pendulum will be

Concept:

• A simple pendulum consists of a heavy particle suspended from a fixed support through a light inextensible string.
• The time period of a simple pendulum: It is defined as the time taken by the pendulum to finish one full oscillation and is denoted by “T”
•  \(T = \frac{2\pi }{\omega } = 2\pi √{\frac{l}{g}}\) -- (1)

Calculation:

Given data, mass of the bob is doubled, m₁ = 2m and the length of the string is halved, l₁ = \(\frac{l}2\)

From equation 1 T ∝ √ l and don't depend upon mass of bob.

Then, \( \frac{T_1}{T} = √\frac{l}{2l}\)

⇒ \(T_1 = \frac{T}{\sqrt2}\)

Additional Information

•  The oscillatory motion of a simple pendulum: Oscillatory motion is defined as the to and fro motion of the pendulum in a periodic fashion and the centre point of oscillation known as equilibrium position
• The amplitude of simple pendulum: It is defined as the distance travelled by the pendulum from the equilibrium position to one side.