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 ______.

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 $$RLC$$ 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