Search for tag: "differential equations"

Lecture 6 Part 3: Driven, damped oscillators

Here we add a driving force to the oscillator and consider how the standard form of the equation is modified. We look at the amplification factor and see what happens under resonant conditions.

From  David Ingram on July 10th, 2020 0 likes 3 plays 0  

Lecture 6 Part 2: Damped oscillators

We extend the ideas from the first part of the lecture to oscillators which include damping effects. Writing the governing equation in a standard form and looking at the meaning of the damping…

From  David Ingram on July 10th, 2020 0 likes 6 plays 0  

Lecture 6 Part 1: Applications of Differential Equations - undamped oscillators

Here we look at how the the same (or a very similar) differential equation applies to several different engineering problems. We consider cantilevers, pendulums and a floating buoy.

From  David Ingram on July 10th, 2020 0 likes 5 plays 0  

Lecture 5 Part 3: Oscillators

Here we look at some more general oscillators and their phase portraits and consider how plotting vector plots can be useful for understanding autonomous systems.

From  David Ingram on July 10th, 2020 0 likes 5 plays 0  

Lecture 5 Part 2: Phase portraits

How do understand the behaviour of the oscillator, why is plotting velocity against displacement useful? What are stationary points and limit cycles?

From  David Ingram on July 10th, 2020 0 likes 9 plays 0  

Lecture 5 Part 1: Van der Pol Oscillator

A look at the behaviour of the van der pol oscillator and its solution using the Runge-Kutta integrator

From  David Ingram on July 10th, 2020 0 likes 8 plays 0  

Lecture 4 Part 4: Methods for real engineering problems

In the last part of the lecture we look at real numerical methods that can be used for real engineering problems. Looking briefly at Runge-Kutta methods and an application modelling methane-air…

From  David Ingram on July 6th, 2020 0 likes 2 plays 0  

Lecture 4 Part 3: State space models

In this part of the lecture we look at how state-space models can be used to solve higher order differential equations using the method for systems of equations.

From  David Ingram on July 6th, 2020 0 likes 1 plays 0  

Lecture 4 Part 2: Systems of equations

In this lecture we look at how the numerical methods can be extended to deal with systems of equations.

From  David Ingram on July 6th, 2020 0 likes 2 plays 0  

Lecture 4 Part 1: Introduction to Numerical Methods

When an analytical solution cannot be found, we can use a numerical method to find an approximate solution. In this lecture we look at Euler's method and explore how it can be used to solver…

From  David Ingram on July 6th, 2020 0 likes 3 plays 0  

Lecture 3 Part 3: But there's no solution...

What happens when the method in the first part of the lecture fails. We look at why and find a way of dealing with the problem.

From  David Ingram on July 6th, 2020 0 likes 3 plays 0  

Lecture 3 Part 2: Complicated Right Hand Sides.

In the second part of this lecture we look at how equations with a complicated right hand side is handled.

From  David Ingram on July 6th, 2020 0 likes 2 plays 0  

Lecture 3 Part 1: Solution of inhomogeneous, linear, differential equations.

In this lecture we extend the ideas in lecture 2 to allow us to solve inhomogeneous equations.

From  David Ingram on July 6th, 2020 0 likes 4 plays 0  

Lecture 2 Part 3: Mass-Spring-Damper

In the last part of this lecture we look at a man-spring damper system (without a driving force) and show how we can solve it using the methods outlined in the first two parts of the lecture. We…

From  David Ingram on July 6th, 2020 0 likes 2 plays 0  

Lecture 2 Part 2: Boundary Conditions

In the second part of this lecture we look at a the use of boundary conditions expressed as both initial value and boundary value problems to find the unknown coefficients in the general solution and…

From  David Ingram on July 6th, 2020 0 likes 3 plays 0  

Lecture 2 Part 1: Solution of homogeneous differential equations

In this lecture we look at a general method for solving homogeneous, linear, differential equations.

From  David Ingram on July 6th, 2020 0 likes 0 plays 0