Question

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8. [10] For the circuit shown, find y(t) using Laplace transform techniques. Assume the initial conditions to be: vel (0-) = 1V, V.2 (0-)=-3V, 112 (0-) = 1mA C1 HI 1uF R6 R4 W 1kΩ Hy(t) 1kΩ x(t) L2 1mH C2 :10F —12V

Answer 1

step: into s-domain Transforming the Voo) = 1/s given circuit dis: 106 R6 јк 27 Q10civity Vesto) = -3's 3x10²s 106 (yes) 109 -315 V Diola step Applying nodal analysis at vils) VIS) - (166) & Vi (s)-12. + V (s) -YES) 10'S 103 vis) this) 103 +Vics) tyls) 1635 us)/ 106 +25 1035 YIS) +12-1 Vils) = YIS) +11 854106 o

at yls) son step3. analysis Applying nodal y (3) - (2) + y(s) - 12 - () + Yes) - Ves) 103 6 10 106 -Vis) Yes 3 10 S +1 100 los - 2 + 125 - 1 106 106 103 106/ -Y(S)-11 254106 +4(s) ast 103 10 06 ^3 +125-1 106. ys) 1660) & (Q3 +10)(254100) 185-4+1 106 S40 3 166 (251106) H3° + (as xid) + (p5x103)+109106 - (18.5-4) (054 18) 44X10 48 + 20100s +19 9 x106)) = 245 +125X166-HX10% + 11x106 >) YUS) 245 + 125x166) 47410 45+ 20020005+ (999x105 YIS) = 6 - 2000 -7 S+500 Applying inverse 3+ (5x165) taplace transform -soot -5x105t - 7e ylt) - 6- 3000e