1. For the electrical circuit shown below: (a) Write the state equations in matrix form. (b) For C = 1, R = 2, and L = 4, find the system eigenvalues and eigenvectors. (c) By simply inspecting the eigenvalues, identify the damped natural frequency, ?d. (d) Again using the eigenvalues, determine the time for the transient response of the system to decay by 90% (i.e. for the homogeneous solution to become roughly 10% of it's initial value)?
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(a) State equations: \begin{aligned} & E_{ij} & = & -{\beta _i} R_{ij} + I_{ji} \\ & {} & {} & {} \\ & & 0 & {} \\ \end{aligned} Show more…
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