Describing Oscillations (CIE A Level Physics)

• An oscillation is defined as follows:

The repetitive variation with time t of the displacement x of an object about the equilibrium position (x = 0)  

   

Pendulum oscillation on a displacement-time graph

A pendulum oscillates between A and B. On a displacement-time graph, the oscillating motion of the pendulum is represented by a wave, with an amplitude equal to x₀

• Equilibrium position (x = 0) is the position when there is no resultant force acting on an object

 

• Displacement (x) of a wave is the distance of a point on the wave from its equilibrium position
  • It is a vector quantity; it can be positive or negative and it is measured in metres (m)

   

• Amplitude (x₀) is the maximum value of the displacement on either side of the equilibrium position and is known as the amplitude of the oscillation
  • Amplitude is measured in metres (m)

 

• Wavelength (λ) is the length of one complete oscillation measured from the same point on two consecutive waves
  • Wavelength is measured in metres (m)

Wavelength and amplitude on a displacement-time graph

Diagram of wavelength and amplitude of a wave

• Period (T) or time period, is the time interval for one complete repetition and it is measured in seconds (s)
  • Simple harmonic oscillations have a constant period
  • Time period can be calculated in terms of both frequency and angular frequency by the equations:

• Where:
  • T = Time period (s)
  • f = frequency (Hz)
  • ω = angular frequency (rad s⁻¹)

Time period on a displacement-time graph

Diagram showing the time period of a wave

• Frequency (f) is the number of oscillations per second measured in hertz (Hz)
  • Hz have the SI units of per second s⁻¹

• Angular Frequency (ω) is the rate of change of angular displacement with respect to time 
  • Angular frequency is measured in rad s⁻¹
  • It is given by the equations:

• Where:
  • ω = angular frequency (rad s⁻¹)
  • T = time period (s)
  • f = frequency (Hz)

Phase difference