Period of Simple Pendulum (AQA A Level Physics): Revision Note

Period of simple pendulum

• A simple pendulum consists of a string and a bob at the end

  • The bob is a weight, generally spherical and considered a point mass

  • The bob moves from side to side

  • The string is light and inextensible remaining in tension throughout the oscillations

  • The string is attached to a fixed point above the equilibrium position

• The time period of a simple pendulum for small angles of oscillation is given by:

$T=2\pi \sqrt{\frac{L}{g}}$

• Where:

  • $T$ = time period (s)

  • $L$ = length of string (from the pivot to the centre of mass of the bob) (m)

  • $g$ = gravitational field strength (N kg^-1)

• The time period of a pendulum does depend on the gravitational field strength, meaning its period would be different on the Earth and the Moon

Small angle approximation

• This formula is limited to small angles ($\theta <10°$) and therefore small amplitudes of oscillation from the equilibrium point

• The restoring force of the pendulum is the weight component acting along the arc of the circle towards the equilibrium position

• It is resolved to act at an angle $\theta$ to the horizontal $x$ 

• When considering SHM because of small angle approximation it is assumed the restoring force acts along the horizontal

• So $\sin \theta \cong \theta$