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Free Vibration of Spring system with two DOF

  1. Mar 22, 2013 #1
    In some questions I am doing, you set of a pair of simultaneous equations and in the notes we have that . For a non trivial solution of X1 and X2,the determinant of
    coefficients of X1 and X2 must be zero.

    An equation might typically look like this [itex](m \omega^2 +k_1)x_1 +k_2 x_2=0[/itex]

    Why must the determinant be zero? When solving SEs in general using matrices, the determinant must be non-zero?
  2. jcsd
  3. Mar 22, 2013 #2


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    For free vibtration, there are no external forces appplied to the system, so the right hand sides of the equations are 0.

    If the determinant is non-zero, the only solution is ##x_1 = x_2 = 0## which is not very interesting!

    The determinant is only zero for "special" values of ##\omega##, and these are the frequencies at which the system can vibrate.
  4. Mar 22, 2013 #3
    Thanks for that. I still don't understand "why" but that is v helpfule.
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