Consider a long, two-wire line composed of solid round conductors. The radius of both conductors is $$0.25$$ cm and the distance between their centers is $$1$$m. If this distance is doubled, then the inductance per unit length.

A single input single output system with $$y$$ as output and $$u$$ as input, is described by $$${{{d^2}y} \over {d{t^2}}} + 2{{dy} \over {dt}} + 10y = 5{{d\,u} \over {dt}} - 3\,u$$$
For the above system find an input $$u(t),$$ with zero initial condition, that produces the same output as with no input and with the initial conditions.
$${{d\,y\left( {{0^ - }} \right)} \over {dt}} = - 4,\,\,\,y\left( {{0^ - }} \right) = 1$$

What is the $$rms$$ value of the voltage waveform shown in Fig?

Fourier Series for the waveform, $$f(t)$$ shown in Fig. is