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Mechanical ad Electrical vibration EASY question please help?

  1. Nov 18, 2009 #1
    Mechanical ad Electrical vibration EASY question please help???

    In Boyce and Diprima textbook it says that:

    mu'' + ku = 0 .

    Then it says the general solution of this is:

    u = Acos (w^2)t + B sin (w^2)t , where w^2 = k/m


    It provides no explanation how it arrives at this. Where does the cos and sin come from?????

    PS: it is supposed to be the greek letter w, whatever that is called and it also has a sub-0 on it, but i didnt include it because it looks confusing without the right fonts.

    please help, thanks
     
  2. jcsd
  3. Nov 18, 2009 #2

    tiny-tim

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    Welcome to PF!

    Hi dwilmer! Welcome to PF! :smile:

    (have a little omega: ω and try using the X2 tag just above the Reply box :wink:)
    Because [cos(ωt)]'' is obviously -ω2cos(ωt), and [sin(ωt)]'' is obviously -ω2sin(ωt) :smile:
     
  4. Nov 18, 2009 #3
    Re: Mechanical ad Electrical vibration EASY question please help???

    Perhaps a more helpful explanation can be found here:

    http://www.stewartcalculus.com/data...ntexts/upfiles/3c3-2ndOrderLinearEqns_Stu.pdf

    page 4 in particular offers a little bit of an explanation, and if you are still confused I would advise reading the entire thing, it isn't too long and is relatively well done.
     
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