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Second derivation function

  1. Jan 15, 2010 #1
    Can someone, please, help me solve this math problem?

    z" / z = k


    z" - second derivative of function z=f(t)


  2. jcsd
  3. Jan 15, 2010 #2
    Re write this as z''-kz=0
    This is a fairly simple constant coeff. ode, solved with a characteristic polynomial.
    If k>0 then you have an exponential solution (two basic solution, one tending to zero and the second grows to infinity)
    If k<0 you have an oscillatory motion, with two basic solution being sine and cosine, and the angular frequency being [tex] \sqrt{|k|} [/tex]
  4. Jan 15, 2010 #3


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    Science Advisor

    And if k= 0, of course, the solution is linear.

    (Just wanted to be complete!:smile:)
  5. Jan 18, 2010 #4
    Thanks for replies
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