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Homework Help: Need help with this problem involving system response

  1. Nov 19, 2007 #1
    1. The problem statement, all variables and given/known data
    Jerry, the “handy-man,” has a shop that makes precision molds, and he wants to be able to produce these molds on site when a client’s product fails. He installs this equipment to the bed of an old truck. Later on, during the summer months, it becomes too unbearably hot to work inside the truck, and he decides to install a fan onto the strengthened roof of the truck. Since Jerry is performing some precision machining in the truck, he wants to make sure the vibration on the truck floor is kept to a minimum. The given system properties are mass m = 1000 kg, spring constant K = 4 x 10^5 N/m, damping coefficient c = 1000 N·s/m, and the harmonic force input f(t) = 0.1cos(20t).

    a) Determine the amplitude of the steady state vibration
    b) Since the steady state vibration is unbearable, suggest/design two ways that can
    fix the problem and keep the amplitude of the vibration less than 1 μm. Which of the two
    methods is more practical? Clearly show all calculations.

    2. Relevant equations
    mx''(t) + cx'(t) + kx(t) = f(t)

    3. The attempt at a solution
    I took the Laplace transformation and found the transfer function and used that to find the steady state response. But I'm not sure about part b) where it asks what can I do to fix the problem.
    Last edited: Nov 19, 2007
  2. jcsd
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