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Free Mechanical Vibrations

  1. Oct 18, 2009 #1
    1. The problem statement, all variables and given/known data
    A mass m=4 is attached to both a spring, with spring constant k=37, and a dash-pot with damping constant c=4.

    The ball is started in motion with initial position x0=1 and initial velocity v0=8 .
    Determine the position function x(t).


    2. Relevant equations



    3. The attempt at a solution
    So, the differential equation would be:
    4x''+4x'+37x=0
    4r^2+4r+37=0
    r=-(1/2)+or- (1/2)sqrt(26)i

    And so,
    x(t)=e^(-.5t)(C1cos(.5sqrt(26)t)+C2sin(.5sqrt(26)t))
    x'(t)=-.5e^(-.5t)(C1cos(.5sqrt(26)t)+C2sin(.5sqrt(26)t))+e^(-.5t)(-.5*C1sqrt(26)sin(.5sqrt(26)t)+.5*C2sqrt(26)cos(.5sqrt(26)t))

    x(0)=C1=1
    x'(0)=.5sqrt(26)C2-.5C1=8
    =.5sqrt(26)C2=17/2
    C2=17/sqrt(26)

    And so,
    x(t)=e^(-.5t)(cos(.5sqrt(26)t)+(17/sqrt(26))sin(.5sqrt(26)t))


    Can anyone see anything wrong with this??
     
  2. jcsd
  3. Oct 19, 2009 #2

    tiny-tim

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    Science Advisor
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    Hi jrsweet! :smile:

    (have a square-root-: √ and try using the X2 tag just above the Reply box :wink:)

    Where did your √26 come from? :confused:
     
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