Edexcel International A Level Physics

Revision Notes

5.21 Period of Simple Harmonic Oscillators

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Period of a simple pendulum

  • A simple pendulum is: 
    • An object moving from side to side
    • Attached to a fixed point above 
  • The time period of a simple pendulum can also be calculated using this equation:

= 2πsquare root of l over g end root

  • Where: 
    • l is the length of the pendulum swing
    • is the strength of gravity on the planet on which the pendulum is set up

Worked example

A child is sitting on a swing that is 200 cm long. What is the period of oscillation?

Step 1: Convert length to meters

200 cm = 2 m

Step 2: Substitute the correct values

= 2πsquare root of l over g end root= 2πsquare root of fraction numerator 2 over denominator 9.81 end fraction end root=2.84 s 

Step 3: Confirm the answer

The time period of 1 oscillation of the swing is 2.84 s

Period of a Mass-Spring System

  • A mass-spring system means:
    • An object moving up and down 
    • On the end of a spring


  • The equation for the restoring force in SHM F = - kx 
    • is the same as the equation for Hooke's Law
  • The time period, T can be calculated using the equation:

T = 2πsquare root of m over k end root

  • Where: 
    • m is the mass of the object on the end of the pendulum
    • k is the spring constant of the material the pendulum is made from

Observing the Motion of a Mass-Spring System

  • An experimental and graphical method can be used to observe the motion of a simple mass-spring system
    • Tie a pencil together with the mass and set the mass in free oscillations by displacing it downwards slightly

  • The oscillations will move the pencil up and down
    • On a piece of graph paper, allow the pencil to trace the path of the oscillations by pulling the paper sideways as the mass-spring system oscillates up and down

  • The oscillations will produce a curved, periodic graph
    • This will decrease in amplitude as the mass-spring system slows down

Mass and spring experiment, downloadable AS & A Level Physics revision notes

The motion of oscillator can be observed through a simple mass and spring system

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