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Vertical 2 mass 2 spring problem - IVP

  1. Dec 12, 2009 #1
    1. The problem statement, all variables and given/known data

    mass1 = 10kg connected to ceiling by a spring
    mass2 = 2kg connected to mass1 by a spring

    2m/s is applied to mass 1 in the downward direction (positive direction) to get the system in motion
    At equilibrium Mass 1 is 2m from the ceiling while mass 2 is 4m from the ceiling

    10 x1’’ = -100x1 + 120(x2-x1)
    2 x2’’ = -120(x2-x1)

    find solution over time period 0<=t<=10sec

    Need to use Eulers method

    2. Relevant equations

    3. The attempt at a solution

    Reduce equations to:
    x1’’ = 12x2-22x1
    x2’’ = 60x1 – 60x2

    x1’ = z
    x1’’ = dz/dx
    z(0) = 2 m/s ????

    x2’ = v
    x2’’ = dv/dt
    v(0) = 0 m/s ?????

    dx1/dx = z = f1(x1,x2,z)
    dz/dx = 12x2-22x1 = f2(x1,x2,z)
    dx2/dx = v = f3(x1,x2,v)
    dv/dx = 60x1 - 60x2 = f4(x1,x2,v)

    Not sure if I have these initial conditions set up properly??
    Please help, Thanks
    Last edited: Dec 12, 2009
  2. jcsd
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