The waveform shown in solid line is obtained by clipping a full-wave rectified sinusoid (shown dashed). The ratio of the rms value of the full-wave rectified waveform to the rms value of the clipped waveform is $\_\_\_\_$ . (Round off to 2 decimal places,)

$$ \text { For the closed-loop system shown, the transfer function } \frac{E(s)}{R(s)} \text { is } $$

Consider a closed loop system as shown.

$$ G_p(s)=\frac{14.4}{s(1+0.1 s)} $$

is the plant transfer function and $G_c(s)=1$ is the compensator. For a unit-step input, the output response has damped oscillations. The damped natural frequency is $\_\_\_\_$ $\mathrm{rad} / \mathrm{s}$. (Round off to 2 decimal places).

The Bode magnitude plot for the transfer function $\frac{V_0(s)}{V_i(s)}$ of the circuit is as shown. The value of $R$ is $\Omega$. (Round off to 2 decimal places)