Understandings: Simple harmonic oscillations, Time period, frequency, amplitude, displacement and phase difference, Conditions for Simple Harmonic Motion
Applications and skill: Qualitatively describing the energy changes taking place during one cycle of an oscillation, Sketching and interpreting graphs of simple harmonic motion examples
Guidance: Graphs describing simple harmonic motion should include displacement– time, velocity–time, acceleration–time and acceleration–displacement, Students are expected to understand the significance of the negative sign in the relationship: a ∝ − x
Data booklet: T = 1/f
An oscillation in physics refers to any regular change in position (or displacement) of an oscillator, or in the value of a measurement. In IB DP Physics we can take regular to mean that the period (the time take for a complete oscillation, usually measured in seconds) and the amplitude (the range between maximum and minimum positions or values) will change only slowly, if at all. Physicists use frequency (number of oscillations per unit time, normally measured in hertz, Hz, or oscillations per second) interchangeably with period.
A good example of a simple oscillating system is the pendulum. Other systems involve springs oscillating either vertically or horizontally.
The word isochronous is used to describe an oscillation with a constant period / frequency. One particular variety of isochronous oscillation in simple harmonic motion. The mathematics of simple harmonic motion is essential for an understanding of many physical, and many non-physical, systems. For a physical system the definition of SHM is that the force on the oscillator, and therefore the acceleration of the oscillator, is proportional to the displacement from the equilibrium position and acts towards the equilibrium position ( a ~ -x ) . This equation, not in the data booklet, is key to understanding the concept of SHM. Basic understanding of SHM is covered here in topic 4, a more detailed look at the mathematics will come in the AHL topic 9. Wave Phenomena.
One concept that can be difficult is the idea of phase and phase difference. Two oscillations are in phase if the oscillate together. Not only must they have the same period / frequency, they must also reach their maximum displacement at the same time and in the same direction.
Oscillators that have the same period but are not in phase are out of phase, and the amount by which they are out of phase is measured in angular units. If the oscillators are opposite (one reaches maximum displacement in one direction at the same moment the other reaches maximum displacement in the other direction) then we can describe them as having a phase difference of π radians, or 180º, out of phase.
If two oscillators have different periods / frequencies then they will have a constantly changing phase difference.
The simulation can be found here: PhET Interactive simulations
Oxford Physics: pages 116 - 123
Hamper HL (2014): pages 150 - 153
Hamper SL: pp 141 - 149 including exercises 1-2 (p 144), 3 (p 146), 4 (p 147), 5-6 (p 148)
Dot Point (4 Oscillations and Waves) questions: pp 175-182