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)

   

• Period (T) or time period, is the time interval for one complete repetition and it is measured in seconds (s)
  • If the oscillations have a constant period, they are said to be isochronous
  • Time period is given by the equation:

  

• 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

• Amplitude (x₀) is the maximum value of the displacement on either side of the equilibrium position 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

• Frequency (f) is the number of oscillations per second and it is measured in hertz (Hz)
  • Hz have the SI units of per second s⁻¹
  • It is given by the equation:

• Where:
  • f = frequency (Hz)
  • T = time period (s)

 

• 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 equation:

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

Phase Difference

• Phase is a useful way to think about waves
• The phase of a wave can be considered in terms of:
  • Wavelength
  • Degrees
  • Radians
• One complete oscillation = 1 wavelength = 360° = 2π radians
• The phase difference between two waves is a measure of how much a point or a wave is in front or behind another
• This can be found from the relative position of the crests or troughs of two different waves of the same frequency
  • When the crests of each wave, or the troughs of each wave are aligned, the waves are in phase
  • When the crest of one wave aligns with the trough of another, they are in antiphase

• The diagram below shows the green wave leads the purple wave by 

An Example of Phase Difference

Two waves ¼ λ out of phase

• In contrast, the purple wave is said to lag behind the green wave by