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


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]


Homogeneous Solution[edit]

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


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



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


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