Introduction
Sections 19.2 and 19.3 have introduced several techniques for solving commonly occurring first-order and second-order ordinary differential equations. In this Section we solve a number of these equations which model engineering systems.
Prerequisites
- understand what is meant by a differential equation
- be familiar with the terminology associated with differential equations: order, dependent variable and independent variable
- be able to integrate standard functions
Learning Outcomes
- recognise and solve first-order ordinary differential equations, modelling simple electrical circuits, projectile motion and Newton’s law of cooling
- recognise and solve second-order ordinary differential equations with constant coefficients modelling free electrical and mechanical oscillations
- recognise and solve second-order ordinary differential equations with constant coefficients modelling forced electrical and mechanical oscillations
Contents
1 Modelling with first-order equations1.1 Applying Newton’s law of cooling
1.2 Modelling electrical circuits
2 Modelling free mechanical oscillations
2.1 Case 1: No damping
2.2 Case 2: Light damping
2.3 Case 3: Heavy damping
3 Modelling forced mechanical oscillations
4 Modelling forces on beams
5 Engineering Example 3
5.1 Shear force and bending moment of a beam
6 Engineering Example 4
6.1 Deflection of a uniformly loaded beam