The spring–mass oscillator

Equipment

• Ideal spring with a hanging mass on a vertical plane
• Sliders for mass m and stiffness k
• Amplitude slider A and a Pause button
• Displacement/force plots and a quantity readout

Procedure

1. Check the linear restoring force

   Run the simulation and Pause at several displacements: the spring force always points toward equilibrium and grows with $|x|$, as $F = -kx$. Change stiffness k and observe that the same displacement yields a different force.

2. Measure the period versus m and k

   At fixed k, raise m through several values and time one full oscillation: the period grows as $\sqrt{m}$. Then raise k at fixed m: the period falls as $1/\sqrt{k}$. Compare each point with $T = 2\pi\sqrt{m/k}$.

3. Verify independence from amplitude

   Hold m, k fixed and change amplitude A: the period must stay the same — the signature of harmonic motion from a linear force. Also watch energy: mechanical energy $E = \frac{1}{2}kA^2$ grows quadratically even though T is constant; predict E before moving A.

Simulation

Experiment history

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