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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 21 "Series RLC circuit.  " }
{XPPEDIT 18 0 "i(t)" "-%\"iG6#%\"tG" }{TEXT -1 20 " is the current and
 " }{XPPEDIT 18 0 "q(t)" "-%\"qG6#%\"tG" }{TEXT -1 15 " is the charge.
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "restart:r:=1; l:=1/100;
 c:=1/100; " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "de1:= diff(i
(t),t)*l+q(t)/c+i(t)*r=sin(w*t);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 23 "de2:=i(t)=diff(q(t),t);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 20 "ini:=i(0)=0, q(0)=0;" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 47 "sol:=dsolve(\{de1,de2,ini\},\{i(t),q(t)\},laplace);" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "sol:=simplify(sol[1]);" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "sol:=subs(exp(-50*t)=0,rhs
(sol));with(plots):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 74 "anim
ate(r*sol,t=0..0.3,w=20..250,frames=100, numpoints=100, color=black );
" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 45 "Now a parallel LC circuit in \+
series with R.  " }{XPPEDIT 18 0 "i1(t)" "-%#i1G6#%\"tG" }{TEXT -1 23 
" is current through L, " }{XPPEDIT 18 0 "q(t)" "-%\"qG6#%\"tG" }
{TEXT -1 20 " is the charge, and " }{XPPEDIT 18 0 "i(t)" "-%\"iG6#%\"t
G" }{TEXT -1 30 " is the current throuth the R." }}}{EXCHG {PARA 0 "" 
0 "" {TEXT -1 41 "Voltage loop containing source, C, and R." }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "restart: de1:=q(t)/c+i(t)*r=
sin(w*t);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 30 "Equal voltages acros
s L and C." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "de2:=l*diff(i
1(t),t)=q(t)/c;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 16 "Currents add t
o " }{XPPEDIT 18 0 "i(t)" "-%\"iG6#%\"tG" }{TEXT -1 1 "." }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "de3:=i1(t)+diff(q(t),t)=i(t);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "ini:=i1(0)=0, i(0)=0, q(0)=0
;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "c:=1/100; l:=1/100; r:
=1;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "sol:=dsolve(\{de1,de
2,de3,ini\}, \{i1(t),i(t),q(t)\}, laplace);" }}}{EXCHG {PARA 0 "" 0 "
" {TEXT -1 74 "Look for the part of sol containing  i(t)...  last time
 I did it it was 3:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "sol:
=simplify(rhs(sol[3]));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "
sol:=subs(exp(-(50)*t)=0,sol)/c;" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 88 "with(plots):animate(r*sol,t=0..0.3, w=20..250, frames
=100, numpoints=100, color=black );" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}}{MARK "23 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 }