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+//Caption:time_response_for_unit_step_function

+//example 6.10.4

+//page 172

+s=%s;

+syms t;

+a=(s+4);

+b=1/(s*(s+2));

+c=(a*b); //in series

+d=0.5;

+e=c/.d

+f=1;

+g=e/.f;

+disp(g,"C(s)/R(s)=");

+disp('for unit step response R(s)=1/s,  so'); 

+h=g*(1/s);

+disp(h,"C(s)=");

+[A]=pfss(h);

+A(1)=(1/s)

+F1=ilaplace(A(1),s,t)

+//A(2)can be written as: A(2)=a1+a2

+a1=-1/(4*(6+3.5*s+s^2));

+a2=(-(s+1.75)/(6+3.5*s+s^2));           

+F2=ilaplace(a1,s,t);

+F3=ilaplace(a2,s,t);

+//now multiplying by their coefficient

+F1=(2/3)*F1;

+F2=(1/6)*F2;

+F3=(2/3)*F3;

+//after adding F1,F2 and F3 and simplyfying we get time response which is denoted by 'c(t)' 

+disp('c(t)=((2-(%e^(-1.75*t)*(2*cos(1.71*t)-0.29*sin(1.71*t))))/3');//time_response
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