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Fundamental- solving a second order differential equation

  1. May 20, 2012 #1
    I've completed my Engineering but doing a self study course in Dynamics of Structures and have got a very fundamnetal question concerning solution of differential equation and hope someone will be able to help me.

    Sorry if its too fundamnetal and stupid!

    Let us say we have to solve a differential equation:

    mu_double_dot + k_u=0

    (double dot indicates second derivative)

    We put,

    u = e^st

    we get first and second order derivative of u and substitute in the abovce differential equation and get:

    s = +i sqrt(k/m) or -i sqrt(k/m)

    We now say that general solution is:

    u = A1 e^s1t + A2 e^s2t

    where s1 and s2 are +i sqrt(k/m) and -i sqrt(k/m) respectively

    Shouldn't the solution be:

    u = e^s1 t OR u = e^s2t ??

    Please can anyone help what is the logic in putting

    u = A1 e^s1t + A2 e^s2t and why?

  2. jcsd
  3. May 20, 2012 #2
    Linear superposition. if y1 and y2 are solutions, then y1 + y2 is also.
  4. May 20, 2012 #3
    Dear Mandlebra,

    Thank you for the response...

    Did you mean:

    If y1 and y2 are solutions then :

    Ay1+By2 are also solutions

    where A and B are constants- did you miss put the A and B in your response?

  5. May 21, 2012 #4
    Yes, I forgot
  6. May 23, 2012 #5
    You are solving the typical equation for a oscillator vibrating.

    You are on the right track.

    But you got imaginary roots.

    what is exp^(i*root).. what is this in terms of trig functions?

    Then it will make sense

    good job,
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