This study guide explores the physical behavior of a simple gravity pendulum experiencing damping (air resistance).
A gravity pendulum consists of a mass (bob) suspended from a pivot by a light cord. When displaced, gravity acts as a restoring force, pulling it back toward its equilibrium position.
In an ideal frictionless environment, the period of a pendulum $T$ depends only on the length of the string $L$ and the acceleration due to gravity $g$:
When air resistance (fluid drag) is present, the amplitude of oscillation decays exponentially over time, dissipating mechanical energy as heat.
The table below demonstrates the relationship between the length of the pendulum ($L$) and its measured period ($T$) over multiple test runs.
| Length (m) | Period (s) | Peak Energy (J) |
|---|---|---|
| 0.5 | 1.42 | 45.2 |
| 1.0 | 2.01 | 38.6 |
| 1.5 | 2.46 | 31.4 |
| 2.0 | 2.84 | 26.8 |
| 2.5 | 3.17 | 20.1 |
| 3.0 | 3.47 | 15.5 |
