Pendulum Amplitudes, from the OnRamps Lab 7 worksheet. Time a pendulum at a small angle and a large angle, then decide whether the period really depends on amplitude. Every run gives new, realistic stopwatch data.
Goal: test whether the period of a pendulum is independent of amplitude by finding the period at a small angle (5° to 15°) and a large angle (20° or more). Start with 3 trials each, then take 10 to 20.
L is measured from the pivot to the center of the bob. t is the stopwatch time for n full oscillations (there and back). Use g = 9.80 m/s². The simple formula assumes a small angle (sin θ ≈ θ). At larger angles the true period is a little longer: T ≈ T₀(1 + θ²/16), θ in radians.
Calibrate your timing. Time one single oscillation at least five times. Your reaction time when starting and stopping the stopwatch adds error to every reading.
Changing L restarts every part, since all your trials must use the same pendulum.
| Trial | Oscillations n | Stopwatch t (s) |
|---|
| Single-period trials | Your answer (s) |
|---|
Use your s from the single-period trials as the timing error of one stopwatch reading. Choose n below; it is also used in Parts 2 and 3.
Draw your own first: ring stand, clamp, string, bob, protractor, the angle, the length L and where you start and stop timing.
Labels that earn the setup points: ring stand and clamp, pivot, protractor centered on the pivot, string length L measured to the bob's center, the dashed vertical (equilibrium), release angle θ, the swing direction, and where timing starts and stops.
Use the course's comparison rule. If either answer is "yes," you cannot say the periods are different. If both are "no," they are different.
Use T ≈ T₀(1 + θ²/16) with θ in radians and T₀ your Part 2 mean (all trials). This check is tighter (0.5%) because the effect is small.