Mathematical Modelling - Block 2 (Mathematical Methods and Models: Block 2)

This block contains units 5-8 Unit 5 Statics; This unit and unit 6 lay the foundations of the subject of mechanics. Mechanics is concerned with how and why objects stay put, and how and why they move. This unit considers how and why they move. This unit assumes a good working knowledge of vectors. Unit 6 Dynamics; Continuing on from Unit 5 this unit considers how and why objects move and outlines the procedure for solving dynamics problems. Unit 7 Oscillations; All around you there are mechanical systems that vibrate or oscillate. Each day you probable experience oscillations in a wide variety of forms: the buzzing of an alarm clock, the vibrations of an electric hair-drier or razor, the sideways movements of a train or boat, and so on. This unit describes a simple experiment involving an oscillating system, introduces Hooke's law as a model for the force exerted by a spring, and goes on to consider how this law applies in various situations where no movement takes place. It also shows how to use Newton's second law to model the oscillations of the simplest oscillating system, which consists of a single particle attached to a single horizontal spring. Unit 8 Energy and Consolidation; This unit consolidates the mechanics covered in the previous units and introduces the topic of energy in mechanical systems.