The circuit shown in Figure P3.21 has an inductor L, a capacitor C, a resistor R, and a voltage source v(t). Considering that L is analogous to a spring, and C is analogous to an inertia, follow the standard steps to obtain the state equations. First sketch the linear graph denoting the currents through and the voltages across the elements L, C, and R by (fl , vl ), (f2, v2) and (f3, v3), respectively, and then proceed in the usual manner
(i) What is the system matrix and what is the input distribution matrix for your choice of state variables?
(ii) What is the order of the system?
(iii) Briefl y explain what happens if the voltage source v(t) is replaced by a current source i(t).
FIGURE P3.21
