5.5.2 Angular Frequency

• Angular frequency, ⍵, in oscillations is equivalent to angular velocity in circular motion 
• It can is defined as:

The rate of change of angular displacement with respect to time

• This can be written as an equation:

• Where:
  • ⍵ = angular frequency (rad s^-1)
  • 2π = circumference of a circle
  • T = time period (s)
  • f = frequency of oscillation (Hz)

Step 1: Consider the motion of the cuckoo

• • The cuckoo goes from being fully compressed to fully extended which means that it travels for an angular displacement of half a circle and not a full circle
  • So, instead of 2π the distance will be π

Step 2: Substitute into the equation for angular velocity and time period

ω = = = 2.09 rad s^-1

Step 3: State the final answer

• • The angular frequency of the cuckoo as it emerges from the clock is 2.1 rad s^-1 (2 s.f.)