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Vibration - Dynamics

  1. May 7, 2009 #1
    1. The problem statement, all variables and given/known data
    Determine the max and min values of x and their times from 0 to 2s
    initial conditions X0 = 0, V0 = 1m/s
    http://img266.imageshack.us/img266/2198/figure1.jpg [Broken]


    2. Relevant equations
    Undamped force vibration:
    m[tex]\ddot{x}[/tex]+kx = F0sin[tex]\omega[/tex]t
    Damped force vibration:
    x = Asin([tex]\omega[/tex]t - [tex]\phi[/tex]) ,where [tex]\phi[/tex]=phase ans A=amplitude
    NB [tex]\omega[/tex] should not be superscripted

    3. The attempt at a solution

    ive drawn a free body diagram as follows
    http://img266.imageshack.us/img266/5150/freebody.jpg [Broken]
    forget to add m[tex]\ddot{x}[/tex] coming off the side.

    resolving forces:
    [tex]\sum[/tex]Fx = m[tex]\ddot{x}[/tex] = -cx - kx + F

    m[tex]\ddot{x}[/tex] + cx + kx = F

    Not sure where to go from here, ultimately i need to plot a graph to show the response of the 10kg mass and see where the max and min distances (x) happen and at what times
     
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. May 7, 2009 #2
    The damping force is proportional to the velocity and not displacement. Then you would solve the 2 homogenous solutions and the steady state solution. You can find how to solve the ODE or the actual solutions on many websites.
     
  4. May 7, 2009 #3
    Many thanks for your reply
    Could you post a link or 2 to help me with this problem please
    hope this doesn't go against forum rules
    Regards
    Tommy100
     
  5. May 7, 2009 #4
    If this is a classical mechanics class, then I am sure your book has solved a very similar problem.
     
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