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# week_05_5.1 - MATH2860U Chapter 5 1 MODELLING WITH HIGHER...

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MATH2860U: Chapter 5 1 MODELLING WITH HIGHER ORDER DIFFERENTIAL EQUATIONS Linear Models: Initial Value Problems (Section 5.1, pg. 182) Recall: We’ve spent the past few classes studying how to solve linear higher-order equations with constant coefficients. In the case of 2 nd order, these are of the form: ) ( t g cy y b y a Let us now explore how such equations arise in a variety of real-life applications. Application: Modelling the motion of a mass on a spring What factors might affect the motion of the mass?

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MATH2860U: Chapter 5 2 We note that there are four separate forces that govern the motion of the mass. 1. Weight: mg w 2. Spring Force: )) ( ( t x s k F s 3. Damping Force: ) ( t x F d 4. External Force: ) ( t F Thus, in order to model the motion of a mass on a spring, we arrive at the equation ) ( ) ( ) ( ) ( t F t kx t x t x m subject to 0 ) 0 ( x x and 1 ) 0 ( x x To begin our study of the motion of the mass on the spring, let us begin with the special
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week_05_5.1 - MATH2860U Chapter 5 1 MODELLING WITH HIGHER...

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