Logarithmic Plot and Approximations Quiz

Which function has the form A sin ωt, where A is its amplitude and ω is its frequency in radians per unit time?

Sine function (correct)
Tangent function
Cosine function
Exponential function

What is the complex conjugate of N = x + jy?

x + jy
-x - jy
x - jy (correct)
-x + jy

What is the magnitude of the complex number N = -2 - 5j / 3 + 4j?

|N| = 5
|N| = 195
|N| = 29 (correct)
|N| = 3

What is the angle of the complex number N = -2 - 5j / 3 + 4j?

φ = 248° (A)

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Which of the following is true about complex numbers as functions of frequency?

Complex numbers as functions of frequency have a magnitude and an angle (B)

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What is the magnitude of the frequency transfer function of a stable LTI system?

The magnitude is the ratio of the sinusoidal steady-state output amplitude over a sinusoidal input amplitude (D)

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What is the phase shift of the steady-state output relative to the input in a stable LTI system?

The phase shift is the angle of the frequency transfer function (C)

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What is the steady-state response of a linear system to a sinusoidal input?

The steady-state response is sinusoidal with the same frequency as the input, but with a different amplitude and phase shift (B)

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According to the text, what is the steady-state response of the system with a frequency of 80 rad/s?

$v2(t) = 5 + 1.59 cos(80t - 1.012)$ (B)

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What happens to the steady-state amplitude of the output as the frequency of the input increases?

It decreases (C)

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What is the relationship between the magnitude ratio M and its decibel equivalent m?

$m = 10 log M^2 = 20 log M dB$ (B)

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What does a negative value of m correspond to in terms of the magnitude ratio M?

$M < 1$, the system attenuates the input (B)

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According to equation (9.1.20), what is the phase angle φ(ω) equal to?

K + tan−1 (τ1 ω) − tan−1 (τ2 ω) (D)

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What are the low-frequency, corner frequency, and high-frequency values of φ(ω) in equation (9.1.20)?

0°, 45°, and 90° (B)

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In equation (9.2.3), what is the expression for the magnitude m(ω) in decibel units?

20 log |K | + 20 log |N1 ( jω)| + 20 log |N2 ( jω)| - 20 log |D1 ( jω)| - 20 log |D2 ( jω)| (D)

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Which of the following is the transfer function for a first order system with numerator dynamics?

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What is the phase angle of the transfer function $T(j\omega) = \frac{4}{5+j\omega}$?

$0.253$ radians (A)

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What is the steady-state response of the system $ẏ + 5y = 4ġ + 12g$ with input $g(t) = 20\sin(4t)$?

$y_{ss}(t) = 62.46\sin(4t + 0.253)$ (C)

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What is the plot of $m(\omega)$ for the transfer function $T(j\omega) = \frac{K(\tau_1\omega j + 1)}{\tau_2\omega j + 1}$?

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 $20\log|K|$. (C)

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According to the text, what is the steady-state response of a system with transfer function $T(j\omega) = \frac{1},{1+j\omega\tau}$?

$y_{ss}(t) = A\sin(\omega t + \phi)$ (D)

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According to the text, what is the phase shift of a system with transfer function $T(j\omega) = \frac{1},{1+j\omega\tau}$?

$\phi = -\tan^{-1}(\omega\tau)$ (C)

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According to the text, what is the magnitude of the transfer function $T(j\omega) = \frac{1},{1+j\omega\tau}$?

$|T(j\omega)| = \frac{1},{\sqrt{1+\omega^2\tau^2}}$ (D)

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According to the text, what is the steady-state response of a system with transfer function $T(j\omega) = \frac{1},{1+j\omega\tau}$ to a sinusoidal input $f(t) = A\sin(\omega t)$?

$y_{ss}(t) = B\sin(\omega t + \phi)$ (B)

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Which of the following is true about periodic inputs?

Periodic inputs are commonly found in many applications. (B)

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What does the term 'frequency response' refer to?

How a system responds to a periodic input. (B)

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What can be determined from the frequency response plots or transfer function of a system?

The steady-state response to a sinusoidal input. (D)

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Which term refers to how a system responds to a periodic input, such as a sinusoid?

Frequency response (D)

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What is the period of a sinusoidal input with a frequency of 60 Hz?

1/60 s (B)

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What can be determined from the frequency response plots or the transfer function of a system?

All of the above (D)

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Which of the following is true about the frequency response of a system?

All of the above. (D)

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What is the period of a sinusoidal input with a frequency of 60 Hz?

1/60 s (C)

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What does the steady-state response of a system depend on?

All of the above (D)

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Which of the following statements is true about the magnitude of the frequency transfer function of a stable LTI system?

It is always positive (D)

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What is the range of possible values for the magnitude of the frequency transfer function of a stable LTI system?

$[0, \infty)$ (B)

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Which of the following can be a possible value for the magnitude of the frequency transfer function of a stable LTI system?

$3.5$ (A)

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What does a magnitude of zero for the frequency transfer function of a stable LTI system indicate?

The system is at rest (D)

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According to equation (9.1.20), what is the phase angle φ(ω) equal to?

$-\arctan(\omega\tau)$ (D)

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What is the relationship between the magnitude ratio M and its decibel equivalent m?

$m = 20\log_{10}(M)$ (A)

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What is the steady-state response of a linear system to a sinusoidal input?

A sinusoidal output with the same frequency but possibly different amplitude and phase (D)

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What happens to the steady-state amplitude of the output as the frequency of the input increases?

It decreases (A)

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Which of the following is the equation of a line in slope-intercept form?

$y = 2x + 3$ (B)

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Which of the following is the equation of a quadratic function?

$y = x^2 - 4x + 3$ (A)

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Which of the following is the equation of a circle?

$(x - 2)^2 + (y + 3)^2 = 4$ (C)

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Which of the following is the equation of a parabola?

$y = x^2 - 4x + 3$ (B)

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Which of the following is the equation of an exponential function?

$y = 2^x$ (A)

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Which of the following is the equation of a logarithmic function?

$y = \log_2{x}$ (A)

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According to equation (9.1.20), what is the phase angle φ(ω) equal to?

K + tan−1 (τ1 ω) − tan−1 (τ2 ω) (B)

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What is the magnitude of the frequency transfer function of a stable LTI system?

|K ||N1 ( jω)||N2 ( jω)|. |D1 ( jω)||D2 ( jω)| (B)

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What is the expression for the magnitude m(ω) in decibel units?

20 log |T ( jω)| = 20 log |K | + 20 log |N1 ( jω)| + 20 log |N2 ( jω)| + · · · − 20 log |D1 ( jω)| − 20 log |D2 ( jω)| − · · · (B)

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According to equation (9.1.20), what is the phase angle φ(ω) equal to?

\arctan(\frac{\tau_2\omega},{1}) (A)

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What is the magnitude of the complex number N = -2 - 5j / 3 + 4j?

\frac{5},{3} (D)

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Which of the following is the transfer function for a first order system with numerator dynamics?

\frac{K(s + \tau_1)},{s(\tau_2 s + 1)} (B)

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Which function has the form A sin ωt, where A is its amplitude and ω is its frequency in radians per unit time?

Trigonometric function (B)

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What is the steady-state response of the system $ẏ + 5y = 4ġ + 12g$ with input $g(t) = 20\sin(4t)$?

\frac{12},{\sqrt{145}}\sin(4t + \arctan(\frac{4},{3})) (A)

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Which of the following best describes the magnitude of the frequency transfer function of a stable LTI system?

The absolute value of the transfer function (A)

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What is the complex conjugate of N = x + jy?

N = x - jy (C)

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Which term refers to how a system responds to a periodic input, such as a sinusoid?

Steady-state response (D)

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What is the relationship between the magnitude ratio M and its decibel equivalent m?

m = 20 \log_{10}(M) (D)

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What is the phase shift of the steady-state output relative to the input in a stable LTI system?

0 degrees (C)

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Which one of these is the phase shift of a system with transfer function $T(j\omega) = \frac{1},{1+j\omega\tau}$?

$-\arctan(\omega\tau)$ (C)

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Which one of these is the steady-state response of a system with transfer function $T(j\omega) = \frac{1},{1+j\omega\tau}$ to a sinusoidal input $f(t) = A\sin(\omega t)$?

$|T(j\omega)|A\sin(\omega t - \arctan(\omega\tau))$ (D)

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Which of the following best describes a Bode plot?

A graph of the frequency response of a system (B)

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What is the purpose of a Bode plot?

To graph the gain and phase-shift plots of a system (A)

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What does a Bode magnitude plot show?

The magnitude (usually in decibels) of the frequency response (C)

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Which of the following is true about the Bode phase plot?

The phase is plotted on a linear vertical axis. (A)

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What is the magnitude of the response of a linear, time-invariant system subjected to an input with frequency ω?

|H(jω)| (D)

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What is the phase shift of the response of a linear, time-invariant system subjected to an input with frequency ω?

arg(H(jω)) (D)

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What is the premise of a Bode plot?

One can consider the log of a function as a sum of the logs of its zeros and poles. (B)

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Logarithmic Plot and Approximations Quiz

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Questions and Answers

Which function has the form A sin ωt, where A is its amplitude and ω is its frequency in radians per unit time?

What is the complex conjugate of N = x + jy?

What is the magnitude of the complex number N = -2 - 5j / 3 + 4j?

What is the angle of the complex number N = -2 - 5j / 3 + 4j?

Which of the following is true about complex numbers as functions of frequency?

What is the magnitude of the frequency transfer function of a stable LTI system?

What is the phase shift of the steady-state output relative to the input in a stable LTI system?

What is the steady-state response of a linear system to a sinusoidal input?

According to the text, what is the steady-state response of the system with a frequency of 80 rad/s?

What happens to the steady-state amplitude of the output as the frequency of the input increases?

What is the relationship between the magnitude ratio M and its decibel equivalent m?

What does a negative value of m correspond to in terms of the magnitude ratio M?

According to equation (9.1.20), what is the phase angle φ(ω) equal to?

What are the low-frequency, corner frequency, and high-frequency values of φ(ω) in equation (9.1.20)?

In equation (9.2.3), what is the expression for the magnitude m(ω) in decibel units?

Which of the following is the transfer function for a first order system with numerator dynamics?

What is the phase angle of the transfer function $T(j\omega) = \frac{4}{5+j\omega}$?

What is the steady-state response of the system $ẏ + 5y = 4ġ + 12g$ with input $g(t) = 20\sin(4t)$?

What is the plot of $m(\omega)$ for the transfer function $T(j\omega) = \frac{K(\tau_1\omega j + 1)}{\tau_2\omega j + 1}$?

According to the text, what is the steady-state response of a system with transfer function $T(j\omega) = \frac{1},{1+j\omega\tau}$?

According to the text, what is the phase shift of a system with transfer function $T(j\omega) = \frac{1},{1+j\omega\tau}$?

According to the text, what is the magnitude of the transfer function $T(j\omega) = \frac{1},{1+j\omega\tau}$?

According to the text, what is the steady-state response of a system with transfer function $T(j\omega) = \frac{1},{1+j\omega\tau}$ to a sinusoidal input $f(t) = A\sin(\omega t)$?

Which of the following is true about periodic inputs?

What does the term 'frequency response' refer to?

What can be determined from the frequency response plots or transfer function of a system?

Which term refers to how a system responds to a periodic input, such as a sinusoid?

What is the period of a sinusoidal input with a frequency of 60 Hz?

What can be determined from the frequency response plots or the transfer function of a system?

Which of the following is true about the frequency response of a system?

What is the period of a sinusoidal input with a frequency of 60 Hz?

What does the steady-state response of a system depend on?

Which of the following statements is true about the magnitude of the frequency transfer function of a stable LTI system?

What is the range of possible values for the magnitude of the frequency transfer function of a stable LTI system?

Which of the following can be a possible value for the magnitude of the frequency transfer function of a stable LTI system?

What does a magnitude of zero for the frequency transfer function of a stable LTI system indicate?

According to equation (9.1.20), what is the phase angle φ(ω) equal to?

What is the relationship between the magnitude ratio M and its decibel equivalent m?

What is the steady-state response of a linear system to a sinusoidal input?

What happens to the steady-state amplitude of the output as the frequency of the input increases?

Which of the following is the equation of a line in slope-intercept form?

Which of the following is the equation of a quadratic function?

Which of the following is the equation of a circle?

Which of the following is the equation of a parabola?

Which of the following is the equation of an exponential function?

Which of the following is the equation of a logarithmic function?

According to equation (9.1.20), what is the phase angle φ(ω) equal to?

What is the magnitude of the frequency transfer function of a stable LTI system?

What is the expression for the magnitude m(ω) in decibel units?

According to equation (9.1.20), what is the phase angle φ(ω) equal to?

What is the magnitude of the complex number N = -2 - 5j / 3 + 4j?

Which of the following is the transfer function for a first order system with numerator dynamics?

Which function has the form A sin ωt, where A is its amplitude and ω is its frequency in radians per unit time?

What is the steady-state response of the system $ẏ + 5y = 4ġ + 12g$ with input $g(t) = 20\sin(4t)$?

Which of the following best describes the magnitude of the frequency transfer function of a stable LTI system?

What is the complex conjugate of N = x + jy?

Which term refers to how a system responds to a periodic input, such as a sinusoid?

What is the relationship between the magnitude ratio M and its decibel equivalent m?

What is the phase shift of the steady-state output relative to the input in a stable LTI system?

Which one of these is the phase shift of a system with transfer function $T(j\omega) = \frac{1},{1+j\omega\tau}$?

Which one of these is the steady-state response of a system with transfer function $T(j\omega) = \frac{1},{1+j\omega\tau}$ to a sinusoidal input $f(t) = A\sin(\omega t)$?

Which of the following best describes a Bode plot?

What is the purpose of a Bode plot?

What does a Bode magnitude plot show?

Which of the following is true about the Bode phase plot?

What is the magnitude of the response of a linear, time-invariant system subjected to an input with frequency ω?

What is the phase shift of the response of a linear, time-invariant system subjected to an input with frequency ω?

What is the premise of a Bode plot?

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