damp Natural frequencies and damping factors. [wn,z] = damp(sys) [wn,z] = damp(P [,dt]) [wn,z] = damp(R [,dt]) sys A linear dynamical system (see syslin). P An array of polynomials. R An array of real or complex floating point numbers. dt A non negative scalar, with default value 0. wn vector of floating point numbers in increasing order: the natural pulsation in rad/s. z vector of floating point numbers: the damping factors. The denominator second order continuous time transfer function with complex poles can be written as s^2 + 2*z*wn*s + wn^2 where z is the damping factor and wn the natural pulsation. If sys is a continuous time system, [wn,z] = damp(sys) returns in wn the natural pulsation \omega_n(in rad/s) and in z the damping factors \xi of the poles of the linear dynamical system sys. The wn and z arrays are ordered according to the increasing pulsation order. If sys is a discrete time system [wn,z] = damp(sys) returns in wn the natural pulsation \omega_n(in rad/s) and in z the damping factors \xi of the continuous time equivalent poles of sys. The wn and z arrays are ordered according to the increasing pulsation order. [wn,z] = damp(P) returns in wn the natural pulsation \omega_n(in rad/s) and in z the damping factors \xi of the set of roots of the polynomials stored in the P array. If dt is given and non 0, the roots are first converted to their continuous time equivalents. The wn and z arrays are ordered according to the increasing pulsation order. [wn,z] = damp(R) returns in wn the natural pulsation \omega_n(in rad/s) and in z the damping factors \xi of the set of roots stored in the R array. If dt is given and non 0, the roots are first converted to their continuous time equivalents. wn(i) and z(i) are the the natural pulsation and damping factor of R(i). The following example illustrates the effect of the damping factor on the frequency response of a second order system. s=%s; wn=1; clf(); Z=[0.95 0.7 0.5 0.3 0.13 0.0001]; for k=1:size(Z,'*') z=Z(k) H=syslin('c',1+5*s+10*s^2,s^2+2*z*wn*s+wn^2); gainplot(H,0.01,1) p=gce();p=p.children; p.foreground=k; end title("$\frac{1+5 s+10 s^2}{\omega_n^2+2\omega_n\xi s+s^2}, \quad \omega_n=1$") legend('$\xi='+string(Z)+'$') plot(wn/(2*%pi)*[1 1],[0 70],'r') Computing the natural pulsations and daping ratio for a set of roots: spec roots