# How to find the stiffness? vibration

1. Nov 23, 2012

### bigbang42

1. The problem statement, all variables and given/known data
a machine of mass 100 tonne generates a simple harmonic disturbing force when operating at a speed of 200rpm. to protect the floor and surrounding machinery it is proposed tp mount the machine on helical springs so that the transmissibility ratio is reduced to 0.1

Q1 determine the total stiffness of the springs required assuming the damping to be negligible ??

I'm having with this question because apparently certain sections you have to make "assumptions" which to me is more like guess work

2. Relevant equations
ωn = sqrt ( k/m)

tr = $\sqrt{(1+(2ζω/ωn)/((1−(ω/ωn)2)2+(2ζω/ωn)2)}$

3. The attempt at a solution

what ive been trying to do is rearrange the transmissibility formula and finding the value of ωn to then use in the ωn = $\sqrt{(k/m)}$ formula to find the stiffness k

although when i do that it gets a little messy and the final value i get looks wrong so i'm not sure if this is the right process to find k in this situation can anyone guide me through it, i just need a good/correct starting point from there on i should be ok

thanks