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System Dynamics problem

  1. Jan 24, 2007 #1
    1. The problem statement, all variables and given/known data
    The problem:
    A fishing boat weighing 147,150 N is towed by a much larger ship. The tow cable is linearly elastic and elongates 0.0278 m for each 1000 N of tension in it. The wave and viscous drag on the fishing boat can be assumed to be linearly proportional to its velocity, and equal to 55,000 N-s/m. At time t=0, the larger tow ship starts moving with constant velocity, V_o = 2 m/s. There is no initial slack in the cable.

    2. Relevant equations

    Fing an expression for the fishing boat displacement, x, as a function of time. Plot the displacement of both boats on the same graph.

    3. The attempt at a solution
    So I have:
    M=147150
    B=55000
    K=(1000/0.0278)=35971 N/m

    The diff-eq I found:
    Mx''+Bx'+Kx=k(V_o)t

    but when I try to solve the diff-eq, I have some non-real number, which doesn't seem right. What should I do?

    Thank you very much!
     
  2. jcsd
  3. Jan 25, 2007 #2

    AlephZero

    User Avatar
    Science Advisor
    Homework Helper

    The general solution of the equation is valid for complex numbers.

    The boundary conditions x(0) and x'(0) are real and all the constants M B K k are real, so the particular solution for this problem has the imaginary part equal to zero.

    To separate the real and imaginary parts, remember that
    e^{iwt} = cos wt + i sin wt
     
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