Pendulum Motion

1. What a Pendulum Is

A pendulum consists of:

  • A cord or string of fixed length

  • A mass at the end called the pendulum bob

When displaced from equilibrium and released, the bob swings back and forth in oscillatory motion.

2. Tension in the Cord

Represented as FtF_tFt​.

Properties:

  • Acts along the cord toward the pivot

  • Keeps the bob moving in an arc

  • Depends on:

    • mass

    • angle of displacement

    • gravitational acceleration

  • Independent of cord material

Restoring Force

The net force from gravity and tension produces a restoring force.

Restoring force:

  • Always points toward the equilibrium position

  • Opposes displacement

Example:

  • If the pendulum moves right, restoring force pulls it back toward center.

Because the bob has momentum, it passes the center and continues to the opposite side.

Energy in a Pendulum

A pendulum constantly exchanges kinetic energy and potential energy.

At the Middle (Equilibrium)

  • Velocity: maximum

  • Kinetic Energy: maximum

  • Potential Energy: zero

At Maximum Displacement (Ends of Swing)

  • Velocity: zero

  • Kinetic Energy: zero

  • Potential Energy: maximum

Energy Conversion

Downward swing:

  • Potential energy → kinetic energy

Upward swing:

  • Kinetic energy → potential energy

Energy continuously transfers between the two forms during oscillation.