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Resonance
26 questions By Tony R. Kuphaldt
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Question 10 of 26
Very interesting things happen to resonant systems when they are “excited” by external sources of oscillation. For example, a pendulum is a simple example of a mechanically resonant system, and we all know from experience with swings in elementary school that we can make a pendulum achieve very high amplitudes of oscillation if we “oscillate” our legs at just the right times to match the swing’s natural (resonant) frequency.
Identify an example of a mechanically resonant system that is “excited” by an external source of oscillations near its resonant frequency. Hint: research the word “resonance” in engineering textbooks, and you are sure to read about some dramatic examples of resonance in action.
Reveal answerLarge buildings have (very low) resonant frequencies, that may be matched by the motion of the ground in an earthquake, so that even a relatively small earthquake can cause major damage to the building.
Challenge question: after researching the behavior of mechanical resonant systems when driven by external oscillations of the same frequency, determine what the effects might be of external oscillations on an electrical resonant system.
Notes:Many, many examples of mechanical resonance exist, some of which are quite dramatic. A famous example of destructive mechanical resonance (of a well-known bridge in Washington state) has been immortalized in video form, and is easily available on the internet. If possible, provide the means within your classroom to display a video clip on computer, for any of the students who happen to find this video file and bring it to discussion.
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Question 11 of 26
If a capacitor and an inductor are connected in series, and energized by an AC voltage source with such a frequency that the reactances of each component are 125 Ω and 170 Ω, respectively, what is the total impedance of the series combination?
Reveal answer45 Ω ∠ 90o
Now, of course, you are wondering: “how can two series-connected components have a total impedance that is less than either of their individual impedances?” Don’t series impedances add to equal the total impedance, just like series resistances? Be prepared to explain what is happening in this circuit, during discussion time with your classmates.
Notes:This question is an exercise in complex number arithmetic, and it is quite counter-intuitive at first. Discuss this problem in depth with your students, so that they are sure to comprehend the phenomenon of series-canceling impedances.
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Question 12 of 26
Calculate all voltage drops and current in this LC circuit at each of the given frequencies:
Frequency VL VC Itotal
50 Hz
60 Hz
70 Hz
80 Hz
90 Hz
100 Hz
Also, calculate the resonant frequency of this circuit.Reveal answer
Frequency VL VC Itotal
50 Hz 0.121 V 0.371 V 1.16 mA
60 Hz 0.221 V 0.471 V 1.77 mA
70 Hz 0.440 V 0.690 V 3.03 mA
80 Hz 1.24 V 1.49 V 7.48 mA
90 Hz 4.25 V 4.03 V 22.8 mA
100 Hz 1.07 V 0.821 V 5.16 mA
fr = 87.6 Hz Notes:This is nothing more than number-crunching, though some students may have found novel ways to speed up their calculations or verify their work.
