In the circuit shown the voltage $${V_{IN}}\,\left( t \right)$$ is described by: $$${V_{IN}}\,\left( t \right) = \left\{ {\matrix{ {0,} & {for\,\,\,t < 0} \cr {15Volts,} & {for\,\,\,t \ge 0} \cr } } \right.$$$

where $$'t'$$ is in seconds. The time (in seconds) at which the current $${\rm I}$$ in the circuit will reach the value $$2$$ Ampere is ______ .

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?