University of Florida/Egm4313/s12.team11.imponenti/R2.9

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Report 2, Problem 9[edit]

Problem Statement[edit]

Find and plot the solution for the L2-ODE-CC corresponding to

with

and initial conditions ,

In another figure, superimpose 3 figs.:(a)this fig. (b) the fig. in R2.6 p.5-6, and (c) the fig. in R2.1 p.3-7

Quadratic Equation[edit]

with

Homogeneous Solution[edit]

The solution to a L2-ODE-CC with two complex roots is given by

where

Solving for A and B[edit]

first initial condition

second initial condition

so the solution to our L2-ODE-CC is

                      

Solution to R2.6[edit]

After solving for the constants and we have the following homogeneous equation

Characteristic Equation and Roots[edit]

We have a real double root

Homogeneous Solution[edit]

We know the homogeneous solution to a L2-ODE-CC with a double real root to be

Assuming object starts from rest

,

Plugging in and applying our first initial condition

Taking the derivative and applying our second condition

Giving us the final solution

                 

Plots[edit]

Solution to this Equation[edit]

Plotr2 9.jpg

Superimposed Graph[edit]

Our solution: shown in blue

Equation for fig. in R2.1 p.3-7: shown in red

Equation for fig. in R2.6 p.5-6: shown in green

R2superposed.jpg

Egm4313.s12.team11.imponenti 03:38, 8 February 2012 (UTC)