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Laplace D.E.

  1. Jun 11, 2012 #1
    Hello , can anyone help me solve this using laplace ?

    mx'' + cx' + kx = 0 , x(0)=0 , x'(0)=0 , m > 0 , c > 0 , k > 0 and c^2-4km > 0


    thanks in advance for your answer.(first time using this forum)
     
  2. jcsd
  3. Jun 11, 2012 #2
    Usually, we like to see what efforts have been put into a solution. It helps us know where you are stuck; it also makes sure we aren't doing all the work for you, which would make the learning process more difficult.

    So please, show what you've done towards a solution so far.
     
  4. Jun 11, 2012 #3
    Hello again and thanks for your answer .
    This is what I got so far :

    mx''+cx'+kx=0 →
    m[s^2 X(s) + sx(0) -x'(0)] + c[sX(s) - x(0)] + kX(s)=0 → ##x(0)=0 , x'(0)=0## →
    X(s)(ms^2+cs+k)=0 →
    since c^2-4km > 0 there are 2 roots a1 and a2.
    Therefore X(s)(s-a1)(s-a2)=0

    and thats where I'm stuck. I know that X(s)=0 is a solution but isnt there anything else?
    (going to sleep now 3:10 am is too late for D.E.)
     
  5. Jun 11, 2012 #4

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    Because the coefficient of x'' is not zero, this problem has a unique solution.
    It is obvious that x identically equal to 0 satisfies this equation so that is the solution.
     
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