How is the frequency of a simple pendulum calculated?

The frequency of a simple pendulum is calculated using the formula f=1/T, where T is the period.

A simple pendulum consists of a mass (bob) attached to a string or rod, which is fixed at a pivot point. When the bob is displaced from its equilibrium position and released, it oscillates back and forth. The time taken for one complete oscillation is called the period, denoted by T.

The frequency of a pendulum is the number of oscillations per unit time, usually measured in hertz (Hz). It is calculated by taking the reciprocal of the period, i.e. f=1/T.

The period of a simple pendulum can be calculated using the formula T=2π√(L/g), where L is the length of the string and g is the acceleration due to gravity. This formula assumes that the amplitude of the oscillation is small (less than 15 degrees).

To calculate the frequency of a simple pendulum, we can substitute the formula for T into the formula for f, giving f=1/(2π√(L/g)). This formula shows that the frequency of a pendulum depends on its length and the acceleration due to gravity.

For example, if the length of a pendulum is 1 metre and the acceleration due to gravity is 9.81 m/s^2, then the frequency of the pendulum is f=1/(2π√(1/9.81))=0.159 Hz. This means that the pendulum oscillates back and forth 0.159 times per second.

A-Level Maths Tutor Summary: The frequency of a simple pendulum, which shows how often it swings back and forth in a second, is found by dividing 1 by its period (T). The period is the time for a full swing and depends on the pendulum's length and gravity's pull. Essentially, to get the frequency, use the formula f=1/(2π√(L/g)), where L is the string's length and g is gravity.