1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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:
    K=(1000/0.0278)=35971 N/m

    The diff-eq I found:

    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


    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
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook