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+//Caption:time_response_for_unit_step_function
+//example 11_8
+//page 476
+s=%s;
+syms t;
+G=(20)/((s+1)*(s+5))
+H=1;
+CL=G/.H
+disp(CL,"C(s)/R(s)=")
+y=ilaplace(CL,s,t);
+disp(y,"c(t)=");
+b=denom(CL)
+c=coeff(b)
+//Wn^2=c(1,1)
+Wn=sqrt(c(1,1))//natural frequency
+//2*zeta*Wn=c(1,2)
+zeta=c(1,2)/(2*Wn)//damping ratio
+Wd=Wn*sqrt(1-zeta^2)//damped frequency
+Mp=(exp(-(zeta*%pi)/sqrt(1-zeta^2)))*100//max. overshoot
+Tp=%pi/Wd//peak time
+t=(2*%pi)/(Wn*sqrt(1-zeta^2))//period of oscillation
+ts=4/(zeta*Wn)//settling time
+N=Wd/(2*%pi)*ts//no. of oscillations completed before reaching steady state
+disp(Tp,"peak time=");
+disp(Mp,"max. peak overshoot=");
+disp(t,"period of oscillation");
+disp(N,"no. of oscillations completed before reaching steady state=");
+disp(ts,"settling time=")