Mass on a Spring: Simple Harmonic Motion
1 · Predict
If you double the mass hanging on the spring, does the oscillation period double?
- The period doubles.
- The period stays the same.
- The period increases, but by less than double.
2 · Set Up
- Open the Mass-on-Spring preset in the Mechanics module. A ball (the bob) hangs from a spring anchored above it.
- Note the speed probe already attached to the bob — it reports the bob's instantaneous speed as it oscillates.
- For each row, set the bob's mass and the spring's stiffness, pull the bob down slightly, release it, and let it oscillate and settle.
3 · Collect Data
| Mass (kg) | Spring constant (N/m) | Period (s) | Equilibrium extension (m) |
|---|---|---|---|
| 0.5 | 30 | ||
| 1 | 30 | ||
| 2 | 30 |
Graph period T (s) against mass m (kg) for your three trials. Is the relationship a straight line? Try graphing T against √m instead — what do you notice?
4 · Analyze
- Using T = 2π√(m/k), calculate the period for each row and compare it to the value you timed in the sandbox.
- Rows 1 and 3 have masses in a 1:4 ratio. By what factor did the period change? Does that match √4 = 2?
5 · Extend
- If you increased the spring constant k instead of the mass, would the period increase or decrease? Sketch the trend you'd expect.
- The bob visibly hangs lower under gravity (equilibrium extension = mg/k), yet gravity g does not appear in T = 2π√(m/k). Explain why the period is unaffected by gravity even though the equilibrium position is.
The Physics Behind This Experiment
Spring Period (SHM)
For a mass oscillating on an ideal spring, the period depends only on the mass and the spring constant — not on amplitude or on gravity.
Kinetic Energy at Equilibrium
The bob's speed is greatest as it passes through the equilibrium point; read that peak speed off the probe to find its kinetic energy there.