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

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
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 .
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
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
Background image of page 2
This is the end of the preview. Sign up to access the rest of the document.

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 ....
View Full Document

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.

Page1 / 2

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

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online