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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=")