printf("closed loop transfer function =16/(s^2+s+16)");
printf("characterstic equation of the given system is s^2+s+16=0");
printf("compare it with the standard second order characterstic equation s^2+2*d*w*s+w^2=0");
w=sqrt(16);
d=0.5/w;
disp(d,"damping ratio=");
disp(w,"undamped natural frequency(in rad/sec)=");
printf("now consider H(s)=1+Ks");
printf("characterstic equation of this system is s^2+(1+16K)*s+16=0");
printf("compare it with the standard second order characterstic equation s^2+2*d*w*s+w^2=0");
d1=0.6;
k=(2*w*d1-1)/16;
disp(k," value of K when d=0.6 is")
pt1=%pi/(w*sqrt(1-d^2));
pt2=%pi/(w*sqrt(1-d1^2));
mo1=exp((-%pi*d)/sqrt(1-d^2))*100;
mo2=exp((-%pi*d1)/sqrt(1-d1^2))*100;
st1=4/(d*w);
st2=4/(d1*w);
disp(pt1,"peak time (in sec) when damping ratio is 0.125:");
disp(pt2,"peak time(in sec) when damping ratio is 0.6:");
disp(mo1,"mAXIMUM OVERSHOOT (in %) when damping ratio is 0.125:");
disp(mo2,"mAXIMUM OVERSHOOT (in %) when damping ratio is 0.6:");
disp(st1,"setlling time(in sec) when damping ratio is 0.125:");
disp(st2,"setlling time (in sec) when damping ratio is 0.:");