(adsbygoogle = window.adsbygoogle || []).push({}); mx''+dx'+kx=constant*t^2*cos(constant*t^2) ???

Hey folks out there.

Im having a problem with this differential equation.

The mathematical model beneath is supposed to describe a nacelle with blades, standing og a tower, as shown in the embedded picture. The stiffness k of the beams are know, aswell as the damping d and the mass m. The unbalance c is also know. What i need to describe, is the first 20 seconds (t=0..20), where the motor starts, and the angular velocity of the nacelle varies linear from 0 up to 10 Hz. The angular velocity is therefore given by omega=Pi [rad/s^2]*t

So now the equations:

mx''+dx'+kx=p(t) where

p(t)=c*Pi^2*t^2*cos(Pi*t^2), t=0..20

All constants are known. I only need to describe the solution for t=0..20.

I seem to get very complex results - and it should indeed be solveable. Any help - links or solutions is very very much appreciated.

Thanks.

Tobias

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# Mx''+dx'+kx=constant*t^2*cos(constant*t^2) ?

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