Version 4
SHEET 1 948 680
WIRE 32 80 -64 80
WIRE 112 80 32 80
WIRE -64 128 -64 80
WIRE 32 128 32 80
WIRE 112 128 112 80
WIRE 32 256 32 208
WIRE -64 352 -64 208
WIRE 32 352 32 336
WIRE 32 352 -64 352
WIRE 112 352 112 192
WIRE 112 352 32 352
WIRE 112 368 112 352
FLAG 112 368 0
FLAG 112 80 C
SYMBOL res -48 224 R180
WINDOW 0 36 76 Left 2
WINDOW 3 36 40 Left 2
SYMATTR InstName R1
SYMATTR Value 1
SYMBOL ind 16 112 R0
SYMATTR InstName L1
SYMATTR Value 200m
SYMBOL cap 96 128 R0
SYMATTR InstName C1
SYMATTR Value 0.5m
SYMBOL voltage 32 240 R0
SYMATTR InstName V1
SYMATTR Value 0
TEXT 184 304 Left 2 !.tran 0 1 0
TEXT 184 264 Left 2 !.ic i(L1) = 0.2m v(C) = 0
TEXT 208 80 Left 2 ;a1^2 = (L/R)^2 = 0.04
TEXT 208 136 Left 2 ;4 a0 a2 = 4 L C = 0.0004
TEXT -696 24 Left 2 ;KCL: V/R + i(L) + i(C) = 0 ... ... (1)
TEXT -632 72 Left 2 ;V = L d i(L)/dt ... ... (2)
TEXT -656 112 Left 2 ;i(C) = C dV/dt ... ... (3)
TEXT -720 176 Left 2 ;Thus, L/R di(L)/dt + i(L) + C dV/dt = 0 ... ... (4)
TEXT -720 232 Left 2 ;Plug (2) into (4): L/R di/dt + i + L C d^2 i/dt^2 = 0
TEXT -720 280 Left 2 ;Re-arrange: L C d^2 i/dt^2 + L/R di/dt + i = 0
TEXT -576 336 Left 2 ;a2 = L C; a1 = L/R; a0 = 1; f(t) = 0.
TEXT 216 200 Left 2 ;a1^2 > 4 a0 a2 ==>> Over-damped