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 one year ago
Solve the initial value problem\[u''+6u'+12u=0\]with \(u(0)=1\) and \(u'(0)=0\)
 one year ago
Solve the initial value problem\[u''+6u'+12u=0\]with \(u(0)=1\) and \(u'(0)=0\)

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modphysnoob
 one year ago
Best ResponseYou've already chosen the best response.3use characteristic equation a^2 + 6a+12 solve for a

abb0t
 one year ago
Best ResponseYou've already chosen the best response.1this is a second order homogeneous differential equation. do you know the general solution? \[y_p = e^{rt}c_1+e^{rt}c_2\]

abb0t
 one year ago
Best ResponseYou've already chosen the best response.1@modphysnoob is correct. except he used "a" so your solution would be: \[y_p = e^{at}c_1+e^{at}c_2\]

johnny0929
 one year ago
Best ResponseYou've already chosen the best response.0I actually have the answer but I am just a little confused about how to do it... It's a spring mass problem and the answer is \[u=e^{3t}cos\sqrt{3}t+\sqrt{3}e^{3t}sin\sqrt{3}t\]

abb0t
 one year ago
Best ResponseYou've already chosen the best response.1then, plug in the initial conditions. take a few derivatives and violê

abb0t
 one year ago
Best ResponseYou've already chosen the best response.1solve for u(0)=1 take the derivative of your particular solution and plug in u(0)=0

johnny0929
 one year ago
Best ResponseYou've already chosen the best response.0ok. when I factor \(a^2+6a+12=0\) I get \((i a+\sqrt{3}3 i) (i a+\sqrt{3}+3 i)\)

modphysnoob
 one year ago
Best ResponseYou've already chosen the best response.3that mean it is sinosoid

johnny0929
 one year ago
Best ResponseYou've already chosen the best response.0which means it's \((\sqrt{3}\pm(3+a)i)=0\) how do i make it look like the general solution?

johnny0929
 one year ago
Best ResponseYou've already chosen the best response.0can you help? because I'm so confused

modphysnoob
 one year ago
Best ResponseYou've already chosen the best response.3hold on, my computer is apparently running on steam engine

modphysnoob
 one year ago
Best ResponseYou've already chosen the best response.3a=3 (+) i* sqrt(3) which is \[Ae^{(3+ i \sqrt{3})t}+Be^{(3 i \sqrt{3})t}\]

modphysnoob
 one year ago
Best ResponseYou've already chosen the best response.3use euler identity and you will get A sin( ) + B cos ()

johnny0929
 one year ago
Best ResponseYou've already chosen the best response.0now i can see it's \[Ae^{3}sin(\sqrt{3}t)+Be^{3}cos(\sqrt{3}t)\]then all i have to do is plug in the initial values, right?

modphysnoob
 one year ago
Best ResponseYou've already chosen the best response.3you are missing t e^(3t)

johnny0929
 one year ago
Best ResponseYou've already chosen the best response.0oh yeah. ok there's a t.

johnny0929
 one year ago
Best ResponseYou've already chosen the best response.0\[u=e^{−3t}cos\sqrt{3}t+\sqrt{3}e^{−3t}sin\sqrt{3}t\]one more question. how do i determine if this equation is over damped, underdamped, or critically damped?

modphysnoob
 one year ago
Best ResponseYou've already chosen the best response.3so sin() and cos(x) just go up and down at t go on

modphysnoob
 one year ago
Best ResponseYou've already chosen the best response.3dw:1362965561866:dw

modphysnoob
 one year ago
Best ResponseYou've already chosen the best response.3while e(3t) dw:1362965602529:dw

modphysnoob
 one year ago
Best ResponseYou've already chosen the best response.3just read it http://en.wikipedia.org/wiki/Damping#Critical_damping_.28.CE.B6_.3D_1.29 it will explain much better than I ever can

johnny0929
 one year ago
Best ResponseYou've already chosen the best response.0oh ok i am reading from my book that all i need to do is compare the coefficient in front of \(u'\) to \(\sqrt{4ac}\) from the equation \(a^2+6a+12=0\)

modphysnoob
 one year ago
Best ResponseYou've already chosen the best response.3crticle damp goes to zero without oscillating under dampm oscillate
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