Damped forced motion and practical resonance In real life things are not as simp

Question

Damped forced motion and practical resonance In real life things are not as simple as they were above. There is, of course, some damping. Our equation becomes for some c > 0. We have solved the homogeneous problem before. We let We replace equation (2.8) with The roots of the characteristic equation of the associated homogeneous problem are . The form of the general solution of the associated homogeneous equation on the sign , or equivalently on the sign of as we have seen before. That is where . In any case, we can see that . Furthermore, be no conflicts when trying to solve for the undermined coefficients by trying A cos (omega B sin ( omega t). Let us plug in and solve for A and B. We get (the tedious details are left to reader) We get that We also compute C = to be Thus our particular solution is Hence we have

Explanation / Answer

%This program solves for the response of
%a damped single degree of freedom system subject to
%a harmonic external force. The expressions used for the
%constants were found by using MAPLE.
%
wdr=3;
wn=3.5;
fo=4;
tf=10;
t=0:tf/1000:tf;
for k=1:3
zeta(k)=input(

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