The figure shows an RLC circuit excited by the sinusoidal voltage $$100cos(3t)$$ Volts, where $$t$$ is in seconds. The ratio $${{amplitude\,\,of\,\,{V_2}} \over {amplitude\,\,of\,\,{V_1}}}\,\,$$ 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 __________.

Consider a single input single output discrete-time system with $$h\left[ n \right]\,$$ as input and $$y\left[ n \right]\,$$ as output, where the two are related as
$$y\left[ n \right]\, = \left\{ {\matrix{ {n\left| {x\left[ n \right]} \right|,} & {for\,\,0 \le n \le 10} \cr {x\left[ n \right] - x\left[ {n - 1} \right],} & {otherwise,} \cr } } \right.$$

Which one of the following statements is true about the system?

A continuous time signal x(t) = $$4\cos (200\pi t)$$ + $$8\cos(400\pi t)$$, where t is in seconds, is the input to a linear time invariant (LTI) filter with the impulse response $$h(t) = \left\{ {{{2\sin (300\pi t)} \over {\matrix{ {\pi t} \cr {600} \cr } }}} \right.\,,\,\matrix{ t \cr t \cr } \,\matrix{ \ne \cr = \cr } \,\matrix{ 0 \cr 0 \cr } $$

Let y(t) be the output of this filter. The maximum value of $$\left| {y(t)} \right|$$ is ________________________.