How can you graphically represent simple harmonic motion?

Simple harmonic motion can be graphically represented using a sine or cosine wave on a displacement-time graph.

In more detail, simple harmonic motion (SHM) is a type of periodic motion where the restoring force is directly proportional to the displacement. It is characterised by its amplitude, frequency, and phase. These characteristics can be represented graphically using a sine or cosine wave, which are the mathematical functions that describe SHM.

The horizontal axis of the graph represents time, while the vertical axis represents displacement from the equilibrium position. The amplitude of the motion is represented by the maximum displacement from the equilibrium position, which corresponds to the peak of the wave on the graph. The frequency of the motion, which is the number of complete cycles per unit time, is represented by the distance between successive peaks (or troughs) on the graph. The phase of the motion, which describes the state of motion at time zero, is represented by the position of the wave on the graph at time zero.

To plot the graph, you would start by determining the amplitude, frequency, and phase of the motion. You would then plot a sine or cosine wave with these characteristics on a displacement-time graph. For example, if the motion has an amplitude of A, a frequency of f, and a phase of φ, you would plot the function A sin(2πft + φ) or A cos(2πft + φ) on the graph.

It's important to note that the choice between a sine and a cosine function depends on the phase of the motion. If the motion starts at the equilibrium position and moves in the positive direction, you would use a sine function. If the motion starts at a peak (or trough) and moves towards the equilibrium position, you would use a cosine function.

For a deeper understanding of simple harmonic motion, including its energy considerations, you might find the explanation of energy in SHM insightful. Moreover, to appreciate how damping affects SHM, the discussion on damping in SHM provides valuable insights. Additionally, the concept of resonance in SHM further elaborates on how external forces can influence the amplitude of the motion.

IB Physics Tutor Summary: Simple harmonic motion, like a pendulum's swing, can be shown using sine or cosine waves on a graph, where time is along the bottom and displacement from the middle position is up the side. The wave's height shows how far it moves, the distance between peaks tells us how often it swings, and where the wave starts tells us about its initial state.