Period of Simple Harmonic Oscillators (Edexcel International A Level (IAL) Physics): Revision Note

Period of a simple pendulum

• A simple pendulum is: 

  • an object moving from side to side

  • attached to a string which is fixed to a point above 

• The period of a simple pendulum can be calculated using the equation:

$T=2\mathrm{\pi }\sqrt{\frac{l}{g}}$

• Where: 

  • $l$ = the length of the pendulum

  • $g$ = the gravitational field strength on the planet on which the pendulum is set up

Period of a Mass-Spring System

• A mass-spring system is:

  • an object moving up and down, or side to side 

  • attached to the end of a spring

• The equation for the restoring force in SHM is the same as the equation for Hooke's law

$F=-kx$

• The time period T can be calculated using the equation:

$T=2\mathrm{\pi }\sqrt{\frac{m}{k}}$

• Where: 

  • $m$ = the mass of the object on the end of the spring

  • $k$ = the spring constant of the spring

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

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