A system is described by the following differential equation, where $$u(t)$$ is the input to the system and $$y(t)$$ is the output of the system. $$$\mathop y\limits^ \bullet \left( t \right) + 5y\left( t \right) = u\left( t \right)$$$

When $$y(0)=1$$ and $$u(t)$$ is a unit step function, $$y(t)$$ is

In the circuit shown in the figure, the value of capacitor C (in mF) needed to have critically damped response i(t) is ______.

A periodic variable x is shown in the figure as a function of time. The root - mean - square (rms) value of x is _______ .

For maximum power transfer between two cascaded sections of an electrical network, the relationship between the output impedance Z₁ of the first section to the input impedance Z₂ of the second section is