30. The current, i, in a series RLC circuit when the switch is closed at can be determined from the solution of the 2nd-order ordinary differential equation

(ODE):

where R, L, and C are the resistance of the resistor, the inductance of the inductor, and the capacitance of the capacitor, respectively.

(a) Solve the equation for i in terms of L, R, C, and t, assuming that at

, , and / .

(b) Use the subs command to substitute H, , and into the expression that was derived in part (a). Make a plot of i versus t for s. (Underdamped response.)

(c) Use the subs command to substitute H, , and into the expression that was derived in part (a). Make a plot of i versus t for s. (Overdamped response.)

(d) Use the subs command to substitute H, , and into the expression that was derived in part (a). Make a plot of i versus t for s. (Critically damped response.)