Simple Harmonic Motion

Guiding Questions

  1. What are the characteristics of periodic motion? How can we study and describe such motion?
  2. How can circular motion be related to simple harmonic motion (SHM)?
  3. How do we analyse simple harmonic motion?

Learning Outcomes (LOs) 

  1. describe simple examples of free oscillations.
  2. investigate the motion of an oscillator using experimental and graphical methods.
  3. understand and use the terms amplitude, period, frequency and angular frequency.
  4. recognise and use the equation a =  - ω2 x as the defining equation of simple harmonic motion.
  5. recall and use x= x0 ω sin( ωt )as a solution to the equation a =  - ω2 x
  6. recognise and use v = v0 cos ( ω t )  ,  v = ± ω ( x 0 2 - x 2 )
  7. describe with graphical illustrations, the changes in displacement, velocity and acceleration during simple harmonic motion.
  8. describe the interchange between kinetic and potential energy during simple harmonic motion.
  9. describe practical examples of damped oscillations with particular reference to the effects of the degree of damping and the importance of critical damping in cases such as a car suspension system.
  10. describe practical examples of forced oscillations and resonance.
  11. describe graphically how the amplitude of a forced oscillation changes with driving frequency near to the natural frequency of the system, and understand qualitatively the factors which determine the frequency response and sharpness of the resonance
  12. show an appreciation that there are some circumstances in which resonance is useful and other circumstances in which resonance should be avoided.

Learning Experiences

  1. Examine representations used in oscillations
  2. Investigate factors affecting period of oscillations using experiments or a simulation
  3. Investigate phase using a turntable or a simulation
  4. Build a model for SHM using a datalogger or simulation
  5. Explore modelling of oscillation in molecules as SHM
  6. Explore benefits and danger of resonance

10. Simple examples of free oscillations LO(a)

10.1 YouTube of many examples of oscillators This video can be used at the start of the first lecture (while students settle down for lecture) to introduce oscillations, to show various modes of oscillations and to interest them.

10.1.1 Example 1: Simple pendulum


Static picture of a pendulum bob given an initial horizontal displacement and released to swing freely to produce to and fro motion

Dynamic picture of a pendulum bob given an initial horizontal displacement and released to swing freely to produce to and fro motion

10.1.2 Run Model:

  1. Run Sim

10.1.2.Q1: what is the maximum angle of release before the motion is not accurately described as a simple harmonic motion for the case of a simple free pendulum?

10.1.2.A1: : 10 degrees for error of , depending on what is the error acceptable, small angle is typically about less than 10 degree of swing from the vertical.