X(t) is a stationary random process with autocorrelation function R_x$$\left( \tau \right)$$= exp$$\left( { - \pi {\tau ^2}} \right)$$. This process is passed through the system shown below. The power spectral density of the output process Y(t) is

The root locus plot for a system is given below. The open loop transfer function corresponding to this plot is given by

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

The input-output transfer function of a plant is h(s)=$${{100} \over {s{{\left( {s + 10} \right)}^2}}}$$. The plant is placed in a unity negative feedback configuration as shown in the figure below. The gain margin of the system under closed loop unity negative feedback is