Simple Harmonic Motion Explorer

Begin with the motion. Make a prediction, then explore the graphs and mathematical models.

Watch first. What do you notice?

A cantilever is fixed at one end and free to bend at the other. Press Play to watch the free tip after it is released.

Dashed line: resting position (equilibrium) Fixed end Tip
Ready to observe

Make a prediction before revealing the graph

  1. What repeats? What changes as you watch?
  2. As the swings become smaller, does the time for one complete back-and-forth motion change? What makes you think so?
  3. Sketch the tip’s displacement from its resting position versus time. Label both axes. Choose upward as positive.

This animation is an idealized model. Your real cantilever measurements will test how well the model describes the experiment.

Hover over or drag a slider to see what that part of the equation does on the graph. Drag across the graph to move through time.

Your curve
t = 0.00 ss(t) = 0.00

Parameters

0.0
3.0
0.80 Hz
0°

Mystery curve challenge

A green band appears on the graph. Read the graph to work out its values, then match it with the sliders.

Where in the cycle?

The arm turns once per cycle. Its height, read off the vertical line, follows the cosine in the equation.

start point, set by φ

0% of the way through a cycle
θ = 2πft + φ = 0.00 rad

Things to try