Differential Equations

Equation Form All simple harmonic motion can be expressed as a differential equation of the form

Solutions Solutions of the differential are of the form where A is the amplitude of the motion, ω is the angular frequency (which equals 2πf) and φ is the phase constant

Mass and Spring

Pendulum Small angle approximation: If θ is measured in radians and is small (less than 20 degrees or so)

Pendulum

Torsional Pendulum A torsional pendulum consists of a rigid body (often a disk) that is suspended by a wire. The pendulum uses the torsion in a twisted wire as the restoring force. The restoring torque in this situation is where κ is the torsion constant and θ is the angular displacement.