Homework5_Solutions

# Homework5_Solutions - MA 107 HW 5 Modeling And Analysis of...

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MA 107 Modeling And Analysis of Dynamic Systems S06 Professor T-C. Tsao HW 5 1. 8.13 Do not use the Laplace Transform method to solve for the response.

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MA 107 Modeling And Analysis of Dynamic Systems S06 Professor T-C. Tsao
MA 107 Modeling And Analysis of Dynamic Systems S06 Professor T-C. Tsao 2. 8.56 Solve for X1(t) and X2(t). Do not use the Laplace Transform method to solve for the response. There are four natural modes: cos(0.69t), sin(0.69t), cos(2.0t), sin (2.0t). The impulse response is the linear combination of these four modes with initial conditions determined below. For X1(s)/F(s) the relative order is 4. Therefore, x1(t) is of C 2 , since the impulse input for f(t) is C -2 . Therefore x1(0+)=x1(0-)=0, Dx1(0+)=Dx1(0-)=0, D 2 x1(0+)=D 2 x1(0-)=0 D 3 x1(0+) is not equals to D 3 x1(0-). We integrate the differential equation to find D 3 x1(0+). Thus, x1(t) = K1 cos(0.69t)+ K2sin(0.69t)+K3 cos(2.0t)+K3 sin (2.0t). Plug in the initial conditions, one can find that x1(t) =

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MA 107 Modeling And Analysis of Dynamic Systems S06 Professor T-C. Tsao For X2(s)/F(s) the relative order is 2.
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Homework5_Solutions - MA 107 HW 5 Modeling And Analysis of...

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