How to find the stiffness? vibration

[bigbang42]

Homework Statement

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

Homework Equations

ωn = sqrt ( k/m)

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

The Attempt at a Solution

what I've 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

 

[KataKoniK]

for your help
Thank you for your post. I understand your confusion with this question and the need for assumptions. we often have to make assumptions in order to simplify a problem and find a solution. In this case, the assumption is that the damping is negligible, which means that we can ignore the effects of damping on the system and focus on the stiffness of the springs.

To determine the total stiffness of the springs required, we can use the formula ωn = √(k/m), where ωn is the natural frequency of the system, k is the stiffness of the springs, and m is the mass of the machine. We can also use the transmissibility ratio formula tr = √[(1+(2ζω/ωn)/((1−(ω/ωn)^2)^2+(2ζω/ωn)^2)], where ζ is the damping ratio, ω is the frequency of the disturbing force, and ωn is the natural frequency.

Since we are assuming that the damping is negligible, we can ignore the term (2ζω/ωn) in the transmissibility formula. This simplifies the formula to tr = √[(1+(2ζω/ωn)/((1−(ω/ωn)^2)^2]. Now, we can rearrange this formula to solve for ωn, which will give us the natural frequency of the system. Once we have ωn, we can use the first formula ωn = √(k/m) to solve for k, the total stiffness of the springs required.

I hope this helps guide you in the right direction. If you still have trouble, please don't hesitate to ask for further clarification or assistance. Keep up the good work as a scientist!