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johnny0929
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Solve the initial value problem\[u''+6u'+12u=0\]with \(u(0)=1\) and \(u'(0)=0\)
 one year ago
 one year ago
johnny0929 Group Title
Solve the initial value problem\[u''+6u'+12u=0\]with \(u(0)=1\) and \(u'(0)=0\)
 one year ago
 one year ago

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

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

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

abb0t Group TitleBest ResponseYou've already chosen the best response.1
solve the quadratic
 one year ago

johnny0929 Group TitleBest ResponseYou've already chosen the best response.0
I 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 \[u=e^{3t}cos\sqrt{3}t+\sqrt{3}e^{3t}sin\sqrt{3}t\]
 one year ago

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

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

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

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

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

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

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

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

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

johnny0929 Group TitleBest ResponseYou've already chosen the best response.0
now 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?
 one year ago

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

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

johnny0929 Group TitleBest 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?
 one year ago

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

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

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

modphysnoob Group TitleBest ResponseYou've already chosen the best response.3
just 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
 one year ago

johnny0929 Group TitleBest ResponseYou've already chosen the best response.0
oh 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 \(a^2+6a+12=0\)
 one year ago

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

johnny0929 Group TitleBest ResponseYou've already chosen the best response.0
thank you!
 one year ago
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