The steady state output of the circuit shown in the figure is given by $$$y\left( t \right) = {\rm A}\left( \omega \right)\sin \left( {\omega t + \phi \left( \omega \right)} \right)$$$

If the amplitude $$\left| {{\rm A}\left( \omega \right)} \right| = 0.25$$, then the frequency $$\omega $$ is

Consider the building block called 'Network N' shown in the figure.
Let $$C = 100\,\mu F\,\,$$ and $$R = 10\,k\Omega $$.

Two such blocks are connected in cascade, as shown in the figure.

The transfer function $${{{V_3}\left( s \right)} \over {{V_1}\left( s \right)}}$$ of the cascaded network is

A series LCR circuit is operated at a frequency different from its resonant frequency. The operating frequency is such that the current leads the supply voltage. The magnitude of current is half the value at resonance. If the values of L, C and R are 1 H, 1 F and 1Ω , respectively, the operating angular frequency (in rad/s) is ________.

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