Pendulum Period Investigation

Students build a simple pendulum and test how string length, bob mass, and release angle affect the time for one swing. The demonstration shows that for small angles the period depends mainly on length, not mass or amplitude.

1. Tie a small mass (washer or metal nut) to a light string and hang it from a fixed support; measure the length from pivot to the center of the bob.
2. Pull the bob to a small angle (about 10 degrees or less) and release without pushing.
3. Use a stopwatch to time 10 full swings, then divide by 10 to find the period; record length and period.
4. Repeat for at least three different lengths, keeping the angle small each time.
5. Test mass: keep length the same but swap bobs of different mass; measure the period again.
6. Test amplitude: keep length and mass the same but release from a larger angle (about 20–30 degrees) and compare the period to the small-angle result.
7. Summarize findings and compare to the model \(T \approx 2\pi\sqrt{L/g}\) for small angles.

Oscillations Demo: Pendulum - Physics Demos:

Simple Pendulum | Science Experiment - Science Projects:

📄 Swinging on a String - ncwit.org: https://www.teachengineering.org/lessons/view/cub_mechanics_lesson09

• Map period squared versus length to show a straight-line relationship.
• Use a smartphone timer or metronome app to reduce timing error; average several trials.
• Build a two-pendulum setup of different lengths to demonstrate phase and beating.
• Explore gravity dependence by comparing results with an online simulator that lets you change g.

• Clear a swing zone so the bob does not strike people or objects.
• Secure the support stand or mounting point so it cannot tip or loosen.
• Use small, smooth masses; avoid sharp edges and do not exceed safe weights for the support.

• Which variable most strongly affects the period for small angles? (String length; longer length gives a longer period following \(T \propto \sqrt{L}\).)
• Does changing the bob mass change the period? (No, mass does not affect period for an ideal pendulum at small angles.)
• Why should the release angle be small for the formula to work well? (The small-angle approximation makes the motion nearly simple harmonic; large angles increase the period slightly.)
• If the length is quadrupled, what happens to the period? (It doubles, because \(T \propto \sqrt{L}\).)
• Where do engineers use pendulums today? (Timing in clocks, tuned mass dampers in buildings, seismology instruments, inertial sensors, and balance systems for robots.)