psheet6

# psheet6 - growth d P d t = aP-bP 2 and some real data taken...

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Data Analysis Modelling and Simulation MATH1711 Epiphany Term Practical Sheet 6 Aim : To investigate two relevant equations in a physical context: 1. A comparison of the continuous logistic model for population growth d P d t = aP - bP 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 t - θ, 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 = y - ky ( t ) - x ( t ) , x (0) y (0) = φ 0 .

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Data Analysis Modelling and Simulation MATH1711 Epiphany Term Practical Sheet 6 Aim : To investigate two relevant equations in a physical context: 1. A comparison of the continuous logistic model for population
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Unformatted text preview: growth d P d t = aP-bP 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 t-θ, 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 = y-ky ( 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.

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psheet6 - growth d P d t = aP-bP 2 and some real data taken...

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