0
$\begingroup$

I would like to transform :

This expression of the transmittance of a 1Dof mechanical system :

T = (k + I c ω)/(k + I c ω - m ω^2)

TO

enter image description here

with

ω0^2 = k/m

and λ = c / (2*m*ω0)

Can you help me to conduct these subsitutions with Mathematica ?

I failed with /. for the moment.

Thank you for your help

$\endgroup$
3
  • $\begingroup$ T //. {ω0 -> k/m, λ -> c / (2*m*ω0)}? $\endgroup$
    – march
    Aug 24, 2017 at 21:58
  • $\begingroup$ @march it doesn't work yet since ω0 is not yet defined in the initial definition of T and the same for λ $\endgroup$
    – Bendesarts
    Aug 24, 2017 at 22:00
  • $\begingroup$ Oh, perhaps you meant T /. {k -> m*ω0, c -> λ*(2*m*ω0)} // Simplify? $\endgroup$
    – march
    Aug 24, 2017 at 22:02

1 Answer 1

1
$\begingroup$

We can get close, but not exactly, by considering the transmittance squared and using a variable r for the ratio ω/ω0.

T = (k + I c ω)/(k + I c ω - m ω^2)
trns2 = T (T /. I -> -I) // Simplify
trns2 = trns2 /. k -> m ω0^2 /. 
    c -> 2 m ω0 λ /. ω -> r ω0 // Simplify
num = Numerator[trns2]
den = Collect[Denominator[trns2], λ, Simplify]
trns = Sqrt[num]/Sqrt[den] /. r -> ω/ω0
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.

Not the answer you're looking for? Browse other questions tagged or ask your own question.