Spring pendulum – simple harmonic motion
PhysicsOscillations & WavesAges 16–17Virtual lab
Use it with your class: students open it from a link or a QR code, with no account needed.
Next in Oscillations & Waves
A mass m attached to a spring of stiffness k is pulled out to amplitude A and released. Watch the mass oscillate and the displacement graph x(t); the period T = 2π√(m/k) updates instantly so you can compare as you change m and k. The Reference circle screen shows a point P moving uniformly round a circle of radius A whose projection moves exactly like the mass, x = A·cos(ωt + φ), with linked x, v and a graphs and an adjustable phase constant φ.
Lesson: Simple harmonic motion, mass–spring system
What it shows
A mass on a spring that is pulled from equilibrium and released performs simple harmonic motion: the restoring force F = −kx makes the acceleration point towards equilibrium, and the period T = 2π√(m/k) does not depend on the amplitude (Hooke's law, no friction). The Reference circle screen shows why x(t) is a cosine curve: a point moving uniformly round a circle of radius A at angular speed ω = √(k/m) has a projection that moves exactly like the mass, x = A·cos(ωt + φ). The point's velocity and centripetal acceleration project onto v and a, and its starting angle is the phase constant φ.
How to use
On Mass on a spring, set the values, predict the period, then press Release / Pause and compare with T. On Reference circle, choose a Phase constant φ and press Reset to see where the motion starts, set Playback to a slower speed and follow how P, its projection, the mass and the x, v and a graphs move together. Change Spring constant k or Mass m and watch ω change, then try the two tasks.
Parameters you can change
- Spring constant 10–200 N/m
- Mass 0.1–2 kg
- Amplitude 1–10 cm
- Show x(t) graph
- Screen Mass on a spring, Reference circle
- Phase constant φ (reference circle) -180–180 °
- Show velocity and acceleration vectors
Questions to explore
- How must you change k or m to halve the period of oscillation?
- Where is point P on the reference circle when the mass moves fastest, and where when its acceleration is greatest?
- Which phase constant φ makes the mass start at O moving in the positive direction?
