anonymous
  • anonymous
check my work (part 2)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
Ok so this time I've studied more pls check my work:) \[\frac{d^2 \vec r}{dt^2}+4\vec r=\vec 0\] Let\[\vec r(t)=\vec Ce^{xt}\] The equation is then... \[\vec C x^2e^{xt}+4 \vec Ce^{xt}=\vec 0\]\[\vec C e^{xt}(x^2+4)=\vec 0\]\[\implies x^2+4=0\]\[x=\pm2i\] \[x_{1}=0+2i\]\[x_{2}=0-2i\]\[\lambda=0\]\[\mu=2\] \[\vec r(t)=\vec C_{1}e^{\lambda t}\cos(\mu t)+\vec C_{2}e^{\lambda t}\sin(\mu t)\]\[\vec r(t)=\vec C_{1}e^0\cos(2t)+\vec C_{2}e^0\sin(2t)\]\[\vec r(t)=\vec C_{1}\cos(2t)+\vec C_{2}\sin(2t)\]
Loser66
  • Loser66
yup
anonymous
  • anonymous
thx :)

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Loser66
  • Loser66
Question: why didn't you go directly from the original equation? Why did you go from the given solution \(\vec r(t) = \vec C e^{xt}\)
Loser66
  • Loser66
What if they don't give you the solution? how can you find it?
anonymous
  • anonymous
I don't understand what you mean ?? you just solve the polynomial and make the equations accordingly if variable is real and distinct, real and same and complex right because IT IS the method for solving the equation, I just didn't take exponential function out of the blue :)
Loser66
  • Loser66
From r" +4r =0 characteristic equation is \(\lambda ^2 +4 =0\) which gives us \(\lambda = \pm 2i\) hence the general solution is as you get \(r = C_1cos(2t) + C_2 sin(2t)\) it is kind of 2-lines solution. That is what I meant.
anonymous
  • anonymous
Oh, But I'm just starting off on this so I'm going slow :)

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