The response of the system $$G\left(s\right)\;=\;\frac{s\;-\;2}{\left(s\;+\;1\right)\left(s\;+\;3\right)}$$ to the unit step input u(t) is y(t). The value of $$\frac{\mathrm{dy}}{\mathrm{dt}}\;\mathrm{at}\;\mathrm t\;=\;0^+\;\mathrm{is}$$ ___________.

A unity negative feedback system has an open–loop transfer function $$G\left(s\right)=\frac K{s\left(s+1\right)}$$.The gain K for the system to have a damping ratio of 0.25 is _____________.

For the second order closed-loop system shown in the figure, the natural frequency (in rad/s) is

The input $$-3\mathrm e^{2\mathrm t}\;\mathrm u\left(\mathrm t\right)$$, where u(t) is the unit step function, is applied to a system with transfer function $$\frac{s-2}{s+3}$$. If the initial value of the output is -2, then the value of the output at steady state is __________.