• 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)??

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

• 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

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)

• 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
• The frequency and the period of the oscillations are related by the following equation:

Phase & 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 is:
  • 1 wavelength
  • 360°
  • 2π radians

Wavelength λ and amplitude A of a travelling wave

• 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 ? λ

Two waves ? λ out of phase

• In contrast, the purple wave is said to?lag?behind the green wave by ? λ
• Phase difference is measured in?fractions of a wavelength, degrees?or?radians
• The phase difference can be calculated from two different points on the same wave or the same point on two different waves
• The phase difference between two points can be described as:
  • In phase?is?360^o?or 2π radians
  • In anti-phase?is?180^o?or π radians

Step 1: Write down the frequency of the child's oscillations?

f?= 0.2 Hz

Step 2: Write down the relationship between the period?T?and the frequency?f

Step 3: Substitute the value of the frequency into the above equation and calculate the period?

T?= 5 s