• An?oscillation?is defined as:

Repeated back and forth movements on either side of any equilibrium position

• When the object stops oscillating, it returns to its equilibrium position
  • An?oscillation?is a more specific term for a vibration
  • An?oscillator?is a device that works on the principles of oscillations
• Oscillating systems can be represented by displacement-time graphs similar to transverse waves
• The shape of the graph is a sine curve
  • The motion is described as?sinusoidal

Properties of Oscillations

• Displacement (x)?of an oscillating system is defined as:

The distance of an oscillator from its equilibrium position

• Amplitude (x₀)?is defined as:

The maximum displacement of an oscillator from its equilibrium position

• Angular frequency (?)?is defined as:

The rate of change of angular displacement with respect to time

• This is a scalar quantity measured in?rad s^-1?and is defined by the equation:

• Frequency (f)?is defined as:

The number of complete oscillations per unit time

• It is measured in Hertz (Hz) and is defined by the equation:

• Time period (T)?is defined as:

The time taken for one complete oscillation, in seconds

• One complete oscillation is defined as:

?The time taken for the oscillator to pass the equilibrium from one side and back again fully from the other side

• The time period is defined by the equation:

• Phase difference?is how much one oscillator is in front or behind another
  • When the relative position of two oscillators are equal, they are?in phase
  • When one oscillator is exactly half a cycle behind another, they are said to be in?anti-phase
  • Phase difference is normally measured in radians or fractions of a cycle
  • When two oscillators are in antiphase they have a phase difference of?π radians

Displacement-time graph of an oscillation of a simple pendulum

Step 1: ??????????

Write down the equation for angular frequency

Step 2: ??????????

Calculate the time period T from the graph

The time period is defined as the time taken for?one complete oscillation

This can be read from the graph:

T = 2.6 ? 0.5 = 2.1 s

Step 3:

Substitute into angular frequency equation