diff options
Diffstat (limited to 'Working_Examples/154/CH17')
4 files changed, 68 insertions, 0 deletions
diff --git a/Working_Examples/154/CH17/EX17.2/DEPENDENCIES/ch17_2.sce b/Working_Examples/154/CH17/EX17.2/DEPENDENCIES/ch17_2.sce new file mode 100755 index 0000000..e9ab99b --- /dev/null +++ b/Working_Examples/154/CH17/EX17.2/DEPENDENCIES/ch17_2.sce @@ -0,0 +1,3 @@ +syms t s ;
+ x=laplace ('3*%e^(2*t)' , t , s ) ;
+ disp (x , " X(s)=" )
diff --git a/Working_Examples/154/CH17/EX17.2/ch17_2.sce b/Working_Examples/154/CH17/EX17.2/ch17_2.sce new file mode 100755 index 0000000..e9ab99b --- /dev/null +++ b/Working_Examples/154/CH17/EX17.2/ch17_2.sce @@ -0,0 +1,3 @@ +syms t s ;
+ x=laplace ('3*%e^(2*t)' , t , s ) ;
+ disp (x , " X(s)=" )
diff --git a/Working_Examples/154/CH17/EX17.4/DEPENDENCIES/ch17_4.sce b/Working_Examples/154/CH17/EX17.4/DEPENDENCIES/ch17_4.sce new file mode 100755 index 0000000..6c4baab --- /dev/null +++ b/Working_Examples/154/CH17/EX17.4/DEPENDENCIES/ch17_4.sce @@ -0,0 +1,31 @@ +clc
+syms t
+s=%s;
+//Factorizing the denominator
+I=(s-10)/((s^2)*(s-%i)*(s+%i));
+disp(I,"I(s)=")
+//The principal part at s=0 is
+//B1/s+B2/s^2
+//Taking the limit s->0 to (s-10)/((s-%i)*(s+%i))
+
+B2=-10
+
+//Taking the limit s->0 to (s*(s-10))/(s^2)*(s^2+1)+(10/s)
+
+B1=1
+
+//The principal part at s=%i is
+//A/(s-%i)
+//Taking the limit s->%i to (s-10)/((s^2)*(s+%i))
+
+A=(-0.5-%i*5)
+
+//As the other co-efficient is conjugate of the above we can write the partial fraction expansion of I(s)
+I=(1/s)-(10/s^2)-(0.5+%i*5)/(s-%i)-(0.5-%i*5)/(s+%i);
+//Taking inverse of each term
+I1=ilaplace('1/s',s,t)
+I2=ilaplace('10/s^2',s,t)
+I3=ilaplace('(0.5+%i*5)/(s-%i)',s,t)
+I4=ilaplace('(0.5-%i*5)/(s+%i)',s,t)
+I=I1-I2-I3-I4
+disp(I,"i(t)=")
diff --git a/Working_Examples/154/CH17/EX17.4/ch17_4.sce b/Working_Examples/154/CH17/EX17.4/ch17_4.sce new file mode 100755 index 0000000..6c4baab --- /dev/null +++ b/Working_Examples/154/CH17/EX17.4/ch17_4.sce @@ -0,0 +1,31 @@ +clc
+syms t
+s=%s;
+//Factorizing the denominator
+I=(s-10)/((s^2)*(s-%i)*(s+%i));
+disp(I,"I(s)=")
+//The principal part at s=0 is
+//B1/s+B2/s^2
+//Taking the limit s->0 to (s-10)/((s-%i)*(s+%i))
+
+B2=-10
+
+//Taking the limit s->0 to (s*(s-10))/(s^2)*(s^2+1)+(10/s)
+
+B1=1
+
+//The principal part at s=%i is
+//A/(s-%i)
+//Taking the limit s->%i to (s-10)/((s^2)*(s+%i))
+
+A=(-0.5-%i*5)
+
+//As the other co-efficient is conjugate of the above we can write the partial fraction expansion of I(s)
+I=(1/s)-(10/s^2)-(0.5+%i*5)/(s-%i)-(0.5-%i*5)/(s+%i);
+//Taking inverse of each term
+I1=ilaplace('1/s',s,t)
+I2=ilaplace('10/s^2',s,t)
+I3=ilaplace('(0.5+%i*5)/(s-%i)',s,t)
+I4=ilaplace('(0.5-%i*5)/(s+%i)',s,t)
+I=I1-I2-I3-I4
+disp(I,"i(t)=")
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