CIE A Level Physics (9702) 2019-2021

Revision Notes

19.1.4 Calculating Speed in SHM

Calculating Speed of an Oscillator

  • The speed of an object in simple harmonic motion varies as it oscillates back and forth
    • Its speed is the magnitude of its velocity
  • The greatest speed of an oscillator is at the equilibrium position ie. when its displacement is 0 (x = 0)
  • The speed of an oscillator in SHM is defined by:

v = v0 cos(⍵t)

  • Where:
    • v = speed (m s-1)
    • v0 = maximum speed (m s-1)
    • ⍵ = angular frequency (rad s-1)
    • t = time (s)
  • This is a cosine function if the object starts oscillating from the equilibrium position (x = 0 when t = 0)
  • Although the symbol v is commonly used to represent velocity, not speed, exam questions focus more on the magnitude of the velocity than its direction in SHM
  • How the speed v changes with the oscillator’s displacement x is defined by:

Calculating Speed of an Oscillator equation 1

  • Where:
    • x = displacement (m)
    • x0 = amplitude (m)
    • ± = ‘plus or minus’. The value can be negative or positive
  • This equation show that when an oscillator has a greater amplitude x0, it has to travel a greater distance in the same time and hence has greater speed v
  • Both equations for speed will be given on your formulae sheet in the exam
  • When the speed is at its maximums (at x = 0), the equation becomes:

v0 = ⍵x0

Worked example: Calculating the speed of a pendulum

Step 1:           

Write out the known quantities

Amplitude of oscillations, x0 = 15 cm = 0.15 m

Displacement at which the speed is to be found, x = 12 cm = 0.12 m

Frequency, f = 6.7 Hz

Step 2:           

Oscillator speed with displacement equation

Calculating Speed of an Oscillator equation 1

Since the speed is being calculated, the ± sign can be removed as direction does not matter in this case

Step 3:           

Write an expression for the angular frequency

Equation relating angular frequency and normal frequency:

⍵ = 2πf = 2π× 6.7 = 42.097…

Step 4:

Substitute in values and calculate

Calculating Speed of an Oscillator Worked equation 2

v = 3.789 = 3.8 m s-1 (2 s.f)

Exam Tip

You often have to convert between time period T, frequency f and angular frequency ⍵ for many exam questions – so make sure you revise the equations relating to these.

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.

Join Save My Exams

Download all our Revision Notes as PDFs

Try a Free Sample of our revision notes as a printable PDF.

Join Now
Go to Top