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

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Report 2, Problem 9[edit | edit source]

Problem Statement[edit | edit source]

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 | edit source]


Homogeneous Solution[edit | edit source]

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


Solving for A and B[edit | edit source]

first initial condition

second initial condition

so the solution to our L2-ODE-CC is


Solution to R2.6[edit | edit source]

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

Characteristic Equation and Roots[edit | edit source]

We have a real double root

Homogeneous Solution[edit | edit source]

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 | edit source]

Solution to this Equation[edit | edit source]

Plotr2 9.jpg

Superimposed Graph[edit | edit source]

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)