Fourier and Laplace 417
Ys
Zs
Ys
RsL sC
s
ss
s
s
Is
Vs
Z
()
()
()
(/ ) ( )
()
()
11
121220132
(()
() ()
s
VsYs
Since
Vs ut
s
()£50[ ()]
50
then
Is
s
s
ss
it I s et
()
() ()
() [(()] si
50
13
50
3
3
13
50
3
22 22
1
⋅
£⋅ nn( )tut⋅ ( ) 3
MATLAB Solution
% Script file : analysis _ RLC
t =-1:0.1:8;t0=0;
u = stepfun(t,t0);
it = 50/3*exp(-t).*sin(3*t).*u;
subplot(2,1,1)
plot(t,it);
title(‘i(t) vs t (numeric solution)’)
xlabel(‘time(sec)’)
ylabel(‘Amplitude (amps)’)
axis([0 6 -4 11])
syms s zs
zs = 2+s+(1/(s*.1));
vs = 50/s;
ILs = vs/zs;
IL = ilaplace(ILs);
disp(‘*******************************************’)
disp(‘ **** symbolic result (sw closes at t=0)*****’)
disp(‘The current i(t) (in amps) is :’)
simIL = simplify(IL);
disp(simIL)
subplot(2,1,2)
ezplot(simIL)
title(‘i(t) vs. t (symbolic solution)’)
axis([0 6 -4 11])
xlabel(‘time(sec)’)
ylabel(‘Amplitude (amps)’)
t0=1;
IL = ilaplace((ILs)*exp(-s)); %sw closes at t=1
disp(‘******* *symbolic result(sw closes at t=1) *****’)
disp(‘The current i(t) (in amps) is given by :’)
simIL = simplify(IL);
disp(simIL)
disp(‘***************************************’)