My Math Forum Diff EQ 2nd Order ODE

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 February 2nd, 2010, 01:00 PM #1 Newbie   Joined: Feb 2010 Posts: 2 Thanks: 0 Diff EQ 2nd Order ODE I just started graduate school in engineering. The class that I am taking is structural dynamics. It's been a number of years since I took diff eq, so I have forgotten quite a bit, though I have been reading my books. I can't seem to find anything that will help me with the homework that my professor has assigned. I hope that there is someone who can help explain things to me. The problem is below. a) find the solution for: m*y''+c*y'+ky=0 i) assume that c=0, y(0)=0, dy/dx (0)=0 Comments: I understand what all this means. The diff eq describes dampened vibrations, with c=0, the equation describes simple harmonic motion. I know what the solution should look like (sin(sqrt(k/m)t)) ii) Assume c=0.5, k=0.5, m=0.5, y(0)=1, dy/dx (0)=0 iii) Assume c=2, k=0.5, m=0.5, y(0)=1, dy/dx =(0)=0 b) find the solution for: m*y''+c*y'+k*y= sin(x) i)Assume c=0.5, k=0.5, m=0.5, y(0)=0, dy/dx (0)=0 Like I said, I understand what all of this means. I remember the concepts but I just don't remember the math to make it happen. I followed one of the examples in my diff eq book and it describes making an auxiliary equation, however, when the coefficients are variables, how am I to solve the resulting quadratic?
 February 2nd, 2010, 01:10 PM #2 Newbie   Joined: Feb 2010 Posts: 2 Thanks: 0 Re: Diff EQ 2nd Order ODE Just noticed I'm in the wrong forum. If one of the mods wants to move this to one of the college math sections, maybe that will help things.
February 2nd, 2010, 07:27 PM   #3
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Quote:
 Originally Posted by foy1der I followed one of the examples in my diff eq book and it describes making an auxiliary equation, however, when the coefficients are variables, how am I to solve the resulting quadratic?
Assume the coefficients are constants and use the quadratic formula. You may need to consider whether the coefficients are positive, zero or negative.

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