Oscillators

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

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

Oscillators

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

Oscillators

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

Oscillators

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

Oscillators

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

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.