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 _______ .

A continuous, linear time - invariant fiilter has an impulse response h(t) described by $$h\left( t \right) = \left\{ {\matrix{ {3\,for\,0 \le t \le 3} \cr {0\,otherwise} \cr } } \right.$$

Whjen a constant input of value 5 is applied to this filter, the steady state output is ____.

A system is described by the following differential equation, where u(t) is the input to the system and y(t) is 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