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Poetria

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## 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)

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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)) :)

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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. :(

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