Pendulum Experiment Summary

Pendulum Overview

  • Pendulums maintain a consistent beat and were historically used in timekeeping.

Factors Affecting Pendulum Period

  • Amplitude of swing: The height from which the pendulum is released.

  • Length of pendulum: Distance from the center of the bob to support.

  • Mass of bob: Weight of the pendulum bob itself.

Experimental Approach

  • Use controlled experiments to isolate variables.

  • Use of Photogate to measure period of swings:

    • Requires changing one variable at a time.

Objectives

  • Measure the pendulum period as a function of:

    • Amplitude

    • Length

    • Bob mass

Preliminary Questions

  1. Does the period depend on string length or amplitude?

  2. Does the period change with different masses?

Procedure Overview

  • Set up the experiment using Vernier equipment.

  • Measure the pendulum period at various amplitudes, lengths, and masses.

Experiment Steps

  • Amplitude Measurements: Swing from minimal angle to ~30°.

  • Length Measurements: Vary from 50 cm to 200 cm with a fixed amplitude of 10°.

  • Mass Measurements: Compare periods using 100 g, 200 g, and 300 g masses with fixed length and amplitude.

Data Collection

  • Record average periods for each condition in specified data tables.

Analysis Questions

  1. Is the interface measuring correctly for the period?

  2. Graph T vs. A, T vs. ℓ, T vs. m: Analyze dependencies on amplitude, length, and mass.

  3. Examine T² vs. ℓ and T vs. ℓ² for direct proportionality.

  4. Investigate period relationship using Newton’s laws.

Extensions

  1. Derive gravitational acceleration g from T² vs. ℓ graph.

  2. Develop guidelines for a reliable pendulum clock under varying temperatures.

  3. Explore large amplitude effects on period and compare against established formulas in textbooks.