Simple Harmonic Pendulum

Mechanical Engineering

How It Works

A simple pendulum consists of a concentrated mass bob suspended from a frictionless pivot by an inextensible cord. In the absence of dissipative friction, the system exchanges potential energy and kinetic energy conservatively under gravity. For small angular displacements, the nonlinear equation of motion linearizes into simple harmonic oscillation with a natural period determined exclusively by pendulum length and gravitational acceleration.

Governing Equation
d²θ / dt² + (g / L) · sin θ = 0 , T₀ ≈ 2π · √(L / g) (for θ ≪ 1 rad)