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Damped Mass Spring System

  1. Apr 26, 2012 #1
    So the equation is x'' + 10x' + 64x = 0
    x(0) = 1
    x'(0) = 0
    I get general solution of e^(-5t)(c1*cos(6.245t) + c2sin(6.245t) )
    From there I get e^(-5t)cos(6.245t)+5e^(-5t)sin(6.245t)
    but it wrong. What the gerbils am I doing wrong?

  2. jcsd
  3. Apr 26, 2012 #2


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    Welcome to PF!

    Hi FHamster! Welcome to PF! :smile:

    (try using the X2 button just above the Reply box :wink:)
    (do hamsters not like gerbils? :biggrin:)

    erm :redface: … haven't you left out a 6.245 ? :wink:
  4. Apr 26, 2012 #3


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    If [itex]y= e^{5t}(c_1cos(6.245t)+ c_2sin(6.245t))[/itex]
    then [itex]y(0)= e^0 (c_1 cos(0)+ c_2 sin(0))= c_1= 1[/itex] so you have that coefficient right.

    [tex]y'= 5e^{5t}(c_1 cos(6.245t)+ c_2 sin(6.245t))+ e^{5t}(-6.245 sin(6.245 t)+6.245cos(6.245t))[/tex]

    [tex]y'(0)= 5e^0(c_1 cos(0)+ c_2 sin(0))+ e^0(-6.245c_1 sin(0)+ 6.245c_2 cos(0))[/tex]
    [tex]y'(0)= 5(c_1)+ (1)(6.245c_2)= 11.245[/tex]
    Knowing that [itex]c_1= 1[/itex], solve for [itex]c_2[/itex].
  5. Apr 29, 2012 #4
    Re: Welcome to PF!

    Thanks, following some of these guidelines and doing some recalcumacations. I managed to get it right

    Hamsters are the masterrace.
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