- #1
Poetria
- 267
- 42
Homework Statement
Consider the spring-mass-dashpot system driven by a sinusoidal force on the mass:
(mD2+bD+k)x=F where sin(omega*t)
Recall that for the unforced underdamped oscillator (b^2<4km, F=0), the value of the natural damped frequency omega_d=sqrt(k/m - b^2/(4m^2)
Find the resonant (angular) frequency omega_r.
That is, find the angular frequency at which the gain of the response attains its maximum.
(This resonant frequency will be in the form sqrt(H) for some expression H. Assume H>0)
----
f(omega)=(k-m*omega^2)^2+b^2*omega^2
f'(omega=-4*m*omega*(k-m*omega^2)+2*b^2*omega=0
I got this one right - sqrt(k/m-b^2/(2*m^2)) :)
---
Now I have a problem:
Finally, what happens if the expression H is negative or zero? Find the angular frequency omega at which the gain attains its maximum for the case when H is less or equal to 0.
Switching signs does not help. :(
----