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Second order differential equation.(Damped oscillation)

  1. Jun 11, 2013 #1
    Hi could do with a little help with this question please!

    The question
    A damped oscillation with no external forces can be modelled by the equation:


    Where x mm is amplitude of the oscillation at time seconds. The initial amplitude of the oscillation is 3mm (i.e. when t=0) and the intial velocity is 5mm/s.
    Solve the equation for x.

    Ok! so far I have;


    [itex] m^2+2m+2=0 [/itex]






    Equating this with m=α±jβ

    Gives α=-1 β=1

    Substituting in to the general solution (complex roots)


    x=3 t=0



    This is the part we are unsure of!


    By the product rule;


    x=0 [itex]\frac{dx}{dt}[/itex]=5



    We know A=3 so therefore B=8


    Is this correct? If not any help would be greatly appreciated.
  2. jcsd
  3. Jun 11, 2013 #2


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    Science Advisor

    Yes, that is correct. I'm not sure why you had any question about it.
  4. Jun 11, 2013 #3
    Just wasn't sure. Followed it from a book from a similar question and don't fully understand it! The question was different enough to have doubts!
  5. Jun 11, 2013 #4
    when you have the solution, you can substitute it into your differential equation to see if you end up with 0.
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