Instrument and springs attached to it

[Imagin_e]

Hi!

I am trying to solve a textbook problem without any success. Fortunately, I found someone that solved it but there is one step that I don't get. Here is a figure showing the problem : https://ibb.co/koatCa

First, we have (I get this part since I found a similar use of it in the book):

X/b=1/|1-(ω/ω_n)²|=0.15/0.10=1.5

And the thing I can't understand is how the person get the following numbers:

For ω<ω_n : ω/ω_n= 0.577
For ω>ω_n: ω/ω_n=1.291

Anyone who can explain?

Thanks!

 

[rude man]

You don't define b but if you're using conventional symbols, b represents damping but there is no damping in this problem.
Anyway, define your symbols.

Would be nice if you could just write F = ma for this problem, then solve a simple ODE to get x(t) as a function of driving frequency and (constant) amplitude.