A $$75$$ MVA, $$10$$ kV synchronous generator has X_d $$= 0.4$$ p.u. The X_d value (in p.u.) is a base of $$100$$ MVA, $$11$$ kV is

Given the relationship between the input $$u(t)$$ and the output $$y(t)$$ to be
$$y\left( t \right) = \int\limits_0^t {\left( {2 + t - \tau } \right){e^{ - 3\left( {t - \tau } \right)}}} u\left( \tau \right)d\tau $$
the transfer function $$Y\left( s \right)/U\left( s \right)$$ is

Consider the voltage waveform $$V,$$ shown in Fig. Find.
$$(a)$$$$\,\,\,\,\,\,\,\,$$ the dc component of $$V,$$
$$(b)$$$$\,\,\,\,\,\,\,\,$$ the amplitude of the fundamental component of $$V,$$ and
$$(c)$$$$\,\,\,\,\,\,\,\,$$ the $$rms$$ value of the ac part of $$V$$