The magnitude of frequency response of an underdamped second order system is 5 at 0 rad/sec and peaks to $${{10} \over {\sqrt 3 }}$$ at 5 $$\sqrt 2 $$ rad/sec. The transfer function of the system is

The impulse response h(t) of a linear time invariant system is given by h(t) = $${e^{ - 2t}}u(t),$$ where u(t) denotes the unit step function.

The frequency response H(ω) of the system in terms of angular frequency 'ω' is given by h( ω)

In the following circuit, the comparator output is logic “I” if V₁ > V₂ and is logic “0” otherwise. The D/A conversion is done as per the relation $$${V_{DAC}} = \sum\limits_{n = 0}^3 {{2^{n - 1}}{b_n}\,\,} Volts,$$$ where b₃(MSB), b₂, b₁ and b₀ (LSB) are the counter outputs.

The counter starts from the clear state.

The stable reading of the LED display is

In the following circuit, the comparator output is logic “I” if V₁ > V₂ and is logic “0” otherwise. The D/A conversion is done as per the relation $$${V_{DAC}} = \sum\limits_{n = 0}^3 {{2^{n - 1}}{b_n}\,\,} Volts,$$$ where b₃(MSB), b₂, b₁ and b₀ (LSB) are the counter outputs.

The counter starts from the clear state.

The magnitude of the error between V_DAC and V_in at steady state in volts is