Mass-Spring Simple Harmonic Motion
A mass on a spring is the standard model for every oscillation in physics. This simulation shows the mass bouncing while plotting displacement against time and tracking how energy shifts between kinetic and potential form.
How to use this simulation
- Change the mass and the spring constant
- Set the starting displacement
- Add damping to watch the oscillation decay
What to look for
- The period is unaffected by how far you pull the mass
- Speed is greatest at the equilibrium point and zero at the extremes
- A stiffer spring or a lighter mass both shorten the period
The physics behind it
The spring exerts a restoring force F = −kx proportional to displacement and directed back towards equilibrium, which is the defining condition for simple harmonic motion. The period is T = 2π√(m/k) and, notably, does not depend on the amplitude. Energy trades between elastic potential ½kx² and kinetic ½mv², with the total staying constant.