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
with
Homogeneous Solution
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The solution to a L2-ODE-CC with two complex roots is given by
where
first initial condition
second initial condition
so the solution to our L2-ODE-CC is
After solving for the constants and we have the following homogeneous equation
Characteristic Equation and Roots
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We have a real double root
Homogeneous Solution
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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
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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)