11. Recall that the charge (Q = Q(t))• on the capacitor of the series LCR circuit drawn below satisfies the equation LQ" + RQ' + Q = E(t) and that charge and current are related by Q'(t) = I(t). ell A series circuit with an inductor (L = 4 henry) and capacitor (C = 0.01 farads) and a resistor with resistance R Ohms (to be determined later!). The charge at t = 0 is 0.02 Coulombs and the current at t = 0 is 2 amperes. There is no impressed voltage so E(t) = = 0. a Write down the initial value problem for the charge at time t Differential equation: Initial conditions: Q(0) = Q'(0)= What should resistance R be to make the system critically damped? Answer: Ohms

11. Recall that the charge (Q = Q(t))• on the capacitor of the series LCR circuit drawn below satisfies the equation LQ" + RQ' + Q = E(t) and that charge and current are related by Q'(t) = I(t). ell A series circuit with an inductor (L = 4 henry) and capacitor (C = 0.01 farads) and a resistor with resistance R Ohms (to be determined later!). The charge at t = 0 is 0.02 Coulombs and the current at t = 0 is 2 amperes. There is no impressed voltage so E(t) = = 0. a Write down the initial value problem for the charge at time t Differential equation: Initial conditions: Q(0) = Q'(0)= What should resistance R be to make the system critically damped? Answer: Ohms