1. Differential Equations

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

3. 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

4. Mass and Spring

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

6. Pendulum

7. 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.