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 __________.

The natural frequency of an undamped second-order system is 40 rad/s. If the system is damped with a damping ratio 0.3, the damped natural frequency in rad/s is ________.

The differential equation $$$100\frac{\mathrm d^2\mathrm y}{\mathrm{dt}^2}-20\frac{\mathrm{dy}}{\mathrm{dt}}+\mathrm y=\mathrm x\left(\mathrm t\right)$$$ describes a system with an input x(t) and an output y(t). The system, which is initially relaxed, is excited by a unit step input. The output y(t) can be represented by the waveform