Vibration: Transmissibility ratio sign change when damping is equal to zero

[Pipsqueakalchemist]

So for the transmissibility ratio equation, after doing a lot of questions when damping is zero and I have to take the square root of the denominator. Some questions take the positive root (1-r^2) while for other questions the solution takes the negative root (r^2-1). Can someone explain when we take the positive or negative root please and thank you

 

[onatirec]

The T.R. is a ratio of force magnitudes and is generally taken as a positive value. So the negative root is taken when r>1.

 

[Lnewqban]

What is the meaning of r in that equation?
Please, see:
https://en.m.wikipedia.org/wiki/Q_factor

 

[onatirec]

It looks like Pipsqueak is no longer with us... Nevertheless, r in the above equation is the ratio between natural frequency and excitation frequency (ω/ω_n). It's a measure of how close the driving frequency is to the resonant frequency, and doesn't provide any explicit information on the damping.

 

[Pipsqueakalchemist]

It looks like Pipsqueak is no longer with us... Nevertheless, r in the above equation is the ratio between natural frequency and excitation frequency (ω/ω_n). It's a measure of how close the driving frequency is to the resonant frequency, and doesn't provide any explicit information on the damping.

Yea I stopped caring about that class so it’s whatever