Loading simulation...
🕒

Simple Pendulum

Beginner

Study the rhythmic oscillations of a mass suspended from a fixed pivot. Discover how period depends on length and gravity, and observe energy transformations between kinetic and potential forms.

Key Formulas

Period (small angle)
T=2πLgT = 2\pi\sqrt{\frac{L}{g}}

Approximate period for small angular displacements using the small-angle approximation.

Angular Frequency
ω=gL\omega = \sqrt{\frac{g}{L}}

Natural angular frequency of oscillation for a simple pendulum.

Potential Energy
U=mgL(1−cos⁡θ)U = mgL(1 - \cos\theta)

Gravitational potential energy relative to the lowest point of the swing.

Equation of Motion
θ¨+gLsin⁡θ=0\ddot{\theta} + \frac{g}{L}\sin\theta = 0

The nonlinear differential equation governing pendulum motion.

Small Angle Approximation
sin⁡θ≈θ(θ≪1)\sin\theta \approx \theta \quad (\theta \ll 1)

Linearization valid for small oscillation amplitudes, enabling analytical solutions.

Key Concepts

  • Simple harmonic motion approximation
  • Small angle approximation
  • Conservation of mechanical energy
  • Period independent of mass
  • Restoring force proportional to displacement
Get a lesson from AeroBotAll Topics