# Determine the stiffness of the springs being installed

1. May 8, 2012

### menco

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)