CIE A Level Physics复习笔记17.1.1 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

• 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