Pendulum Motion

Pendulum motion is the movement of a weight swinging freely from a pivot. Wolfram|Alpha provides formulas for calculating this harmonic motion for a large range of pendulum types from double pendulums to torsion pendulums. Wolfram|Alpha includes the equations of motion and Lagrangians for these different systems.

Pendulum

Visualize and calculate the motion of a simple pendulum for both small and large oscillations.

Analyze the motion of a simple pendulum:

Find equations associated with a pendulum:

Determine the trajectory of a pendulum:

Spring Pendulum

Compute the properties, such as frequency and period of motion, of a pendulum hung from a spring.

Analyze the motion of a spring pendulum:

Double Pendulum

Explore the motion of a double pendulum, or a pendulum hung from another pendulum.

Analyze the motion of a double pendulum:

Coupled Pendulum

Examine the motion of a system of two pendulums that are mode locked.

Analyze the motion of a coupled pendulum:

Find the Lagrangian of a system:

RELATED EXAMPLES

  • Dynamical Systems
  • Physical Principles
  • Torsion Pendulum

    Calculate the properties of a torsion, or twisting, pendulum.

    Analyze the motion of a torsion pendulum: