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Homework Help: Determine the stiffness of the springs being installed

  1. May 8, 2012 #1
    1. The problem statement, all variables and given/known data
    You are tasked to reduce the vibrations of of an old air conditioning unit through the structure of a building. To do this you intend to mount the fan unit on 4 free-standing spring isolators with a non skid base. By choosing the appropriate springs and configuration you will be able to reduce the natural frequency of the system by a factor of 5 which will reduce the vibrations by 96%. The combined mass of the fan unit and spring system is 570kg and the fan operates at a frequency of 1750 rpm, determine the stiffness of the springs being installed.

    2. Relevant equations

    w = 2(pi)f
    w = sqrt(k/m)

    3. The attempt at a solution

    So I start by converting rpm to hz which gives me 29.2 hz for f.

    I divide the mass of the system by 4 due to it having 4 springs which will give me 142.5kg

    Next I find the angular frequency

    w = 2(pi)(29.2)
    = 183.469 rad/s (then divide this by a factor of 5? to reduce the vibrations)
    = 36.6938 rad/s

    then put all of this into the final formula to find k

    w = sqrt(k/142.5)
    k = 142.5(36.6938)^2
    = 195502 Nm (1.955x10^5 Nm)
  2. jcsd
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