In the circuit shown, the positive angular frequency $$\omega$$ (in radians per second) at which magnitude of the phase difference between the voltages $$V_1$$ and $$V_2$$ equals $$\frac{\mathrm\pi}4$$ radians, is __________.

In the circuit shown, $$V$$ is a sinusoidal voltage source. The current $$I$$ is in phase with voltage $$V$$. The ratio $${{{\rm{Amplitude of voltage across the capacitor }}} \over {{\rm{Amplitude of voltage across the resistor }}}}$$ is ______.

The figure shows an $$RLC$$ circuit with a sinusoidal current source.

At response, the ratio $$\left| {{{\rm I}_L}} \right|/\left| {{{\rm I}_R}} \right|$$, i.e., the ratio of the magnitudes of the inductor current phasor and the resistor current phasor, is _________.

In the $$RLC$$ circuit shown in the figure, the input voltage is given by v_i(t) = 2 cos(200t)+4 sin(500t). The output voltage v₀(t) is