2. Time-Domain Representations of LTI Systems

2.10 SolvingDifferential and Difference EquationsExample 2.22: RC Circuit (continued): Complete ResponseFind the complete response of the RC circuit depicted in Fig. 2.30 toan input x(t) = cos(t)u(t) V, assuming normalized values R = 1 and C = 1 F and assuming that the initial voltage across thecapacitor is y(0 ) = 2 V.1. Homogeneous sol. :2. Particular solution: p 1RCy t cos2 t sin2 t V1 RC 1 RC 3. Complete solution : 0= 1R = 1 , C = 1 F4. Coefficient c 1 determined by I.C. : y(0 ) = y(0+ )0 1 1 12 ce cos0 sin 0 c c = 3/22 2 2Time-Domain Representations ofLTI Systems5. Final solution:70