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exidez
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Homework Statement
http://img27.imageshack.us/img27/2193/matlapassig2fig.jpg
http://img132.imageshack.us/img132/7126/matlapassig2.jpg
Homework Equations
My impulse response is entirely different which make me believe that i have messed up my ODE. I have taken the laplace tranform to get it into the from of y to f
The Attempt at a Solution
[tex]m_{s}\frac{d^{2}y}{dt^{2}}-c(\frac{dy}{dt} - \frac{dy1}{dt}) + k(y - y1)=0[/tex]
[tex]m_{u}\frac{d^{2}y1}{dt^{2}}+c(\frac{dy1}{dt} - \frac{dy}{dt}) + k(y1 - y) +k_{t}(y1-f(t))=0[/tex]
Laplace Transform:
[tex]Y(S)(m_{s}s^{2}-sc+k)+Y1(S)(sc-k)=0[/tex]
[tex]Y1(S)(m_{u}s^{2}+sc+k+k_{t})+Y(S)(-sc-k)-F(S)k_{t}=0[/tex]
Rearranging First Eqn:
[tex]Y(S)\frac{m_{s}s^{2}-sc+k}{sc-k}=-Y1(S)[/tex]
Substitution:
[tex]-Y(S)\frac{m_{s}s^{2}-sc+k}{sc-k}(m_{u}s^{2}+sc+k+k_{t})+Y(S)(-sc-k)=F(S)k_{t}[/tex]
[tex]-Y(S)(s^{4}(m_{u}m_{s})+s^{3}cm_{s}+s^{2}m_{s}k+s^{2}m_{s}k_{t}-s^{3}cm_{u}-s^{2}c^{2}-sck-sck_{t}+s^{2}m_{u}k+csk+k^{2}+kk_{t}+Y(S)(-c^{2}s^{2}+k^{2}=F(S)(sck_{t}-kk_{t}[/tex]
[tex]Y(S)(-s^{4}(m_{u}m_{s})-s^{3}(cm_{s}-cm_{u})-s^{2}(m_{s}k+m_{s}k_{t}+m_{u}k+s(ck_{t})-kk_{t})=F(S)(sck_{t}-kk_{t})[/tex]
So to get the transform from y to f we want this right?
[tex]\frac{sck_{t}-kk_{t}}{-s^{4}(m_{u}m_{s})-s^{3}(cm_{s}-cm_{u})-s^{2}(m_{s}k+m_{s}k_{t}+m_{u}k+s(ck_{t})-kk_{t}}[/tex]
When substituting the values in from the question my impulse response done through MATLAB doesn't look anything like the one given in the question...Have i done something wrong?
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