Mathematical Modelling - Block 5 (Mathematical Methods and Models: Block 5)

This block contains units 17 - 20 Unit 17 Damping, Forcing and Resonance; This unit refers back to the contents of several earlier units. In particular it builds upon and extends the model of simple harmonic motion and uses this approach in analysing one-dimensional motion. It also returns to the concept of a resistance force proportional to the velocity of a particle. Unit 18 Normal Modes; This unit continues with the theme of mechanics, in particular, it builds on earlier units that dealt with oscillations. In order to solve the equations of motion derived for the mechanical systems studied, it uses the methods used for solving systems of differential equations. This unit also draws heavily on the discussions regarding eigenvalues and eigenvectors. Unit 19 Systems of Particles; The main objective of this unit is to show how to obtain useful information on the complicated motion of an object or system, and demonstrates that the concept of centre of mass is crucial to this process. Unit 20 Circular Motion; The theme of this unit is rotational motion. It concentrates mainly on analysing the circular motion of a particle. This can be used to model a wide range of situations, such as a child on a swing, the pendulum of a clock and a chair-o-plane roundabout at a fairground. This unit builds on many of the ideas from earlier units mainly: polar coordinates, vectors, torque and Newton's second law.