Solution General Method for Circuit Analysis (Cookbook Method for Circuit Analysis [1]) 1. Find the initial current in each inductor and the initial voltage across each capacitor. 2. Write the integro-differential equations for the circuit using the mesh method or the nodal method: a. It may be helpful to simplify the network first-combine elements in series or parallel, Thevenin equivalent, Norton equivalent, etc. b. Differentiate, if necessary, to remove integral terms. c. Combine the mesh or node equations algebraically to eliminate all but the desired dependent variable.
Result : a 0 dny d n -1 y dy + a1 n -1 + ...... + a n -1 + a n y = f (t ) n dt dt dt
(I)
3. Using the result from part (1) and the mesh or node equations, find all
of the necessary initial conditions - i.e. evaluate the equations at t = 0+. An nth order equation require will n initial conditions.
Initial Conditions : y (0 + ), dy + d n -1 y (0 ),...... n -1 (0 + ) dt dt
(II)
4. If f(t) 0, find the forced (steady state) response (yforced) using the
method of undetermined coefficients. 5. Set f(t) = 0 and solve the resulting homogeneous equation for the natural (transient) response-assume ytransient = k1est, substitute into the differential equation (I) to obtain the characteristic equation, solve for the n roots of the characteristic equation and write the ap...