Oscillators  

Dynamical system maps

The map of phase space of a dynamical system is a really convenient way of summarising the behaviour of a system. In particular it doesn't require a solution to the equations of motion.

Oscillators  

Resonance

When an oscillator is driven at just the right frequency it hits resonance and absorbs energy from the driving. The details of resonance for a driven and damped harmonic oscillator are explored.

Oscillators  

Energy in a Damped Harmonic Oscillator

Energy of the damped harmonic oscillator is described. The Q of an oscillator.

Oscillators  

Driven and Damped Oscillator

The solution to a damped oscillator with a periodic driving force is derived.

Oscillators  

Damped Harmonic Oscillator

The solutions to the harmonic oscillator with a velocity dependant drag force are derived. The relaxation time for the oscillator is defined.

Oscillators  

Lotka-Voltera Equations

The Lotka-Voltera equations are a very simple model of predator-prey dynamics. They lead to oscillatory behaviour in both populations.

Oscillators  

The Pendulum

The equations of motion and solutions are derived for the simple pendulum and a general pendulum. Dynamical maps are introduced as a way of handling nonlinear oscillators.

Oscillators  

Harmonic Oscillator

The motion for a harmonic oscillator is derived using Newton's second law. Different parametrizations of the solution, the velocity, acceleration and energy are also determined.