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Unformatted text preview: growth d P d t = aPbP 2 and some real data taken from the US census oﬃce; 2. The motion of a pendulum(s). The practical is self contained an available via the AiM server, however it is implicit that you know how a second order (or for that matter a fourth order equation) can be expressed as a system of two (or four) equations. For example, suppose that a damped pendulum is modelled by the equation d 2 θ d t 2 =k d θ d tθ, θ (0) = φ, θ ± (0) = 0 then setting x ( t ) = θ ( t ) and y ( t ) = θ ± ( t ) it follows that d x d t = θ ± = y ( t ) , d y d t = θ ±± =ky ( t )x ( t ) , x (0) = φ, y (0) = 0 . or d x d t d y d t = yky ( t )x ( t ) , x (0) y (0) = φ ....
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This note was uploaded on 02/04/2011 for the course MATH 1711 taught by Professor Dru.picchini during the Spring '11 term at Durham.
 Spring '11
 DrU.Picchini
 Equations

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