Simple pendulum

Definition

A simple pendulum consists of a mass (called the bob) attached to the end of a string or rod of fixed length, which swings freely in a vertical plane under the influence of gravity. It exhibits periodic motion with its restoring force proportional to the sine of its displacement angle.

5 Must Know Facts For Your Next Test

1. The period of a simple pendulum is given by $T = 2\pi \sqrt{\frac{L}{g}}$, where $L$ is the length of the string and $g$ is the acceleration due to gravity.
2. Simple pendulums exhibit simple harmonic motion for small angular displacements (typically less than 15 degrees).
3. The frequency of a simple pendulum is inversely proportional to its period, given by $f = \frac{1}{T}$.
4. Air resistance and friction at the pivot point can cause damping, leading to gradual energy loss and decreased amplitude over time.
5. The maximum kinetic energy occurs at the lowest point in its swing, while maximum potential energy occurs at the highest points.

Review Questions

• What is the formula for calculating the period of a simple pendulum?
• Under what condition does a simple pendulum exhibit simple harmonic motion?
• How do air resistance and friction affect the motion of a simple pendulum?

Related terms

Period:

The time taken for one complete cycle of oscillation.

Frequency:

The number of oscillations per unit time, typically measured in Hertz (Hz).

Simple Harmonic Motion:

A type of periodic motion where the restoring force is directly proportional to displacement and acts in the direction opposite to that displacement.