The figure shows the single line diagram of a power system with a double circuit transmission line. The expression for electrical power is $$\,1.5\,\,\sin \delta ,\,\,$$ where $$\delta $$ is the rotor angle. The system is operating at the stable equilibrium point with mechanical power equal to $$1$$ pu. If one of the transmission line circuits is removed, the maximum value of $$\delta ,$$ as the rotor swings is $$1.221$$ radian. If the expression for electrical power with one transmission line circuit removed is $$\,{P_{\max }}\,\sin \delta ,\,\,$$ the valueof $${P_{\max }}\,,$$ in pu is _________.

The positive, negative and zero sequence reactances of a wye-connected synchronous generator are 0.2 pu, 0.2 pu, and 0.1 pu, respectively. The generator is on open circuit with a terminal voltage of 1 pu. The minimum value of the inductive reactance, in pu, required to be connected between neutral and ground so that the fault current does not exceed 3.75 pu if a single line to ground fault occurs at the terminals is _______ (assume fault impedance to be zero). (Give the answer up to one decimal place)

Let the signal $$$x\left(t\right)=\sum_{k=-\infty}^{+\infty}\left(-1\right)^k\delta\left(t-\frac k{2000}\right)$$$ be passed through an LTI system with frequency response $$H\left(\omega\right)$$, as given in the figure below The Fourier series representation of the output is given as

Consider $$$g\left(t\right)=\left\{\begin{array}{l}t-\left\lfloor t\right\rfloor,\\t-\left\lceil t\right\rceil,\end{array}\right.\left.\begin{array}{r}t\geq0\\otherwise\end{array}\right\}$$$ where $$t\;\in\;R$$
Here, $$\left\lfloor t\right\rfloor$$ represents the largest integer less than or equal to t and $$\left\lceil t\right\rceil$$ denotes the smallest integer greater than or equal to t. The coefficient of the second harmonic component of the Fourier series representing g(t) is _________.