# 17.1.1 Describing Oscillations

### Describing Oscillations

• 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

• 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

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

#### Exam Tip

The properties used to describe oscillations are very similar to transverse waves. The key difference is that oscillators do not have a ‘wavelength’ and their direction of travel is only kept within the oscillations themselves rather than travelling a distance in space. ### Author: Katie

Katie has always been passionate about the sciences, and completed a degree in Astrophysics at Sheffield University. She decided that she wanted to inspire other young people, so moved to Bristol to complete a PGCE in Secondary Science. She particularly loves creating fun and absorbing materials to help students achieve their exam potential.
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