The simple pendulum

Equipment

• Virtual simple pendulum with a small bob and light inextensible string
• Length slider l (20–200 cm)
• Sliders for initial angle and g value
• T²-versus-l plot and a period readout

Procedure

1. Measure the period at different lengths

   Keep the initial angle small, drag l through 4–5 values, and read T at each point. Plotting $T^2$ versus l gives a straight line of slope $4\pi^2/g$, matching $T \approx 2\pi\sqrt{l/g}$.

2. Test the small-angle condition

   Hold l fixed and increase the initial angle from ~5° upward: the period grows slightly beyond the $2\pi\sqrt{l/g}$ prediction, since $\sin\theta \approx \theta$ holds only at small angles. Record the deviation to see the approximation's limit.

3. Infer and change g

   From a measured (l, T) pair, compute $g = 4\pi^2 l/T^2$ and compare with the g slider value. Then change g (e.g., another planet): the period must scale as $T \propto 1/\sqrt{g}$ — halving g raises T by $\sqrt{2}$; predict before checking.

Simulation

Experiment history

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