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

1. Open the Mass-on-Spring preset in the Mechanics module. A ball (the bob) hangs from a spring anchored above it.
2. Note the speed probe already attached to the bob — it reports the bob's instantaneous speed as it oscillates.
3. 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

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

1. Using T = 2π√(m/k), calculate the period for each row and compare it to the value you timed in the sandbox.
2. 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

1. If you increased the spring constant k instead of the mass, would the period increase or decrease? Sketch the trend you'd expect.
2. 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

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