The classical theory for oscillations and waves at a second year university level.

Oscillatory behaviour is ubiquitous in Nature, and in particular the harmonic oscillator is one of the cornerstone models of physics. This material is used at Macquarie University in the unit *phys201 Physics IIA* where it forms the first half.

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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.

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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.

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Oscillators

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

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Oscillators

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

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Oscillators

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

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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.

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Oscillators

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

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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.

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Coupled Oscillators

Coupling together two or more oscillators introduces a whole new level of complexity. It turns out that there is a particular way of looking at the system that makes it simple to solve the motion.

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Coupled Oscillators

The loaded string is a classic problem of coupled oscillators where \(N\) small masses are threaded onto a light string. It makes a nice transition for considering the continuum case and waves.

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Coupled Oscillators
Waves

The continuum limit of the loaded string is derived, arriving at the one dimensional wave equation.