Logarithmic Plot and Approximations Quiz

<p>φ = 248°</p> Signup and view all the answers

<p>Complex numbers as functions of frequency have a magnitude and an angle</p> Signup and view all the answers

<p>The magnitude is the ratio of the sinusoidal steady-state output amplitude over a sinusoidal input amplitude</p> Signup and view all the answers

<p>The phase shift is the angle of the frequency transfer function</p> Signup and view all the answers

<p>The steady-state response is sinusoidal with the same frequency as the input, but with a different amplitude and phase shift</p> Signup and view all the answers

<p>$v2(t) = 5 + 1.59 cos(80t - 1.012)$</p> Signup and view all the answers

<p>It decreases</p> Signup and view all the answers

<p>$m = 10 log M^2 = 20 log M dB$</p> Signup and view all the answers

<p>$M &lt; 1$, the system attenuates the input</p> Signup and view all the answers

<p>K + tan−1 (τ1 ω) − tan−1 (τ2 ω)</p> Signup and view all the answers

<p>0°, 45°, and 90°</p> Signup and view all the answers

<p>20 log |K | + 20 log |N1 ( jω)| + 20 log |N2 ( jω)| - 20 log |D1 ( jω)| - 20 log |D2 ( jω)|</p> Signup and view all the answers

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<p>$0.253$ radians</p> Signup and view all the answers

<p>$y_{ss}(t) = 62.46\sin(4t + 0.253)$</p> Signup and view all the answers

<p>The plot of $m(\omega)$ is obtained by subtracting the plot of $\tau_2s + 1$ from that of $\tau_1s + 1$, with a scale adjustment of $20\log|K|$.</p> Signup and view all the answers

<p>$y_{ss}(t) = A\sin(\omega t + \phi)$</p> Signup and view all the answers

<p>$\phi = -\tan^{-1}(\omega\tau)$</p> Signup and view all the answers

<p>$|T(j\omega)| = \frac{1},{\sqrt{1+\omega^2\tau^2}}$</p> Signup and view all the answers

<p>$y_{ss}(t) = B\sin(\omega t + \phi)$</p> Signup and view all the answers

<p>Periodic inputs are commonly found in many applications.</p> Signup and view all the answers

<p>How a system responds to a periodic input.</p> Signup and view all the answers

<p>The steady-state response to a sinusoidal input.</p> Signup and view all the answers

<p>Frequency response</p> Signup and view all the answers

<p>1/60 s</p> Signup and view all the answers

<p>All of the above</p> Signup and view all the answers

<p>All of the above.</p> Signup and view all the answers

<p>1/60 s</p> Signup and view all the answers

<p>All of the above</p> Signup and view all the answers

<p>It is always positive</p> Signup and view all the answers

<p>$[0, \infty)$</p> Signup and view all the answers

<p>$3.5$</p> Signup and view all the answers

<p>The system is at rest</p> Signup and view all the answers

<p>$-\arctan(\omega\tau)$</p> Signup and view all the answers

<p>$m = 20\log_{10}(M)$</p> Signup and view all the answers

<p>A sinusoidal output with the same frequency but possibly different amplitude and phase</p> Signup and view all the answers

<p>It decreases</p> Signup and view all the answers

<p>$y = 2x + 3$</p> Signup and view all the answers

<p>$y = x^2 - 4x + 3$</p> Signup and view all the answers

<p>$(x - 2)^2 + (y + 3)^2 = 4$</p> Signup and view all the answers

<p>$y = x^2 - 4x + 3$</p> Signup and view all the answers

<p>$y = 2^x$</p> Signup and view all the answers

<p>$y = \log_2{x}$</p> Signup and view all the answers

<p>K + tan−1 (τ1 ω) − tan−1 (τ2 ω)</p> Signup and view all the answers

<p>|K ||N1 ( jω)||N2 ( jω)|. |D1 ( jω)||D2 ( jω)|</p> Signup and view all the answers

<p>20 log |T ( jω)| = 20 log |K | + 20 log |N1 ( jω)| + 20 log |N2 ( jω)| + · · · − 20 log |D1 ( jω)| − 20 log |D2 ( jω)| − · · ·</p> Signup and view all the answers

<p>\arctan(\frac{\tau_2\omega},{1})</p> Signup and view all the answers

<p>\frac{5},{3}</p> Signup and view all the answers

<p>\frac{K(s + \tau_1)},{s(\tau_2 s + 1)}</p> Signup and view all the answers

<p>Trigonometric function</p> Signup and view all the answers

<p>\frac{12},{\sqrt{145}}\sin(4t + \arctan(\frac{4},{3}))</p> Signup and view all the answers

<p>The absolute value of the transfer function</p> Signup and view all the answers

<p>N = x - jy</p> Signup and view all the answers

<p>Steady-state response</p> Signup and view all the answers

<p>m = 20 \log_{10}(M)</p> Signup and view all the answers

<p>0 degrees</p> Signup and view all the answers

<p>$-\arctan(\omega\tau)$</p> Signup and view all the answers

<p>$|T(j\omega)|A\sin(\omega t - \arctan(\omega\tau))$</p> Signup and view all the answers

<p>A graph of the frequency response of a system</p> Signup and view all the answers

<p>To graph the gain and phase-shift plots of a system</p> Signup and view all the answers

<p>The magnitude (usually in decibels) of the frequency response</p> Signup and view all the answers

<p>The phase is plotted on a linear vertical axis.</p> Signup and view all the answers

<p>|H(jω)|</p> Signup and view all the answers

<p>arg(H(jω))</p> Signup and view all the answers

<p>One can consider the log of a function as a sum of the logs of its zeros and poles.</p> Signup and view all the answers