Suppose you're given the circuit shown below, with R = 40 Q.C = 100 µF, and L = 400 mH. The input is Vin, and the output is Vout Assume that Vin is a step input and no energy is initially store in the capacitor. Hint: See lecture 15, slide 10. L R Vin C: Vou out a) Calculate the undamped natural frequency of this system, in rad/s. Answer: rad/s b) Now convert your answer from (a) to Hz. Answer: Hz c) Calculate the damping ratio of this system. Answer:

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Suppose you're given the circuit shown below, with R = 40 Q.C = 100 µF, and L = 400 mH.
The input is Vin, and the output is Vou Assume that Vin is a step input and no energy is initially store
in the capacitor.
Hint: See lecture 15, slide 10.
L R
Vin
Vou
out
C:
a) Calculate the undamped natural frequency of this system, in rad/s.
Answer:
rad/s
b) Now convert your answer from (a) to Hz.
Answer:
Hz
c) Calculate the damping ratio of this system.
Answer:
d) Will the output voltage exhibit oscillations under the step input? If so, at what frequency, in rad/s?
Answer:
rad/s
e) Suppose we want to change the circuit to have a peak time of 30 ms (0.03 s). What damped natural
frequency would be required, in rad/s?
Answer:
rad/s
Transcribed Image Text:Suppose you're given the circuit shown below, with R = 40 Q.C = 100 µF, and L = 400 mH. The input is Vin, and the output is Vou Assume that Vin is a step input and no energy is initially store in the capacitor. Hint: See lecture 15, slide 10. L R Vin Vou out C: a) Calculate the undamped natural frequency of this system, in rad/s. Answer: rad/s b) Now convert your answer from (a) to Hz. Answer: Hz c) Calculate the damping ratio of this system. Answer: d) Will the output voltage exhibit oscillations under the step input? If so, at what frequency, in rad/s? Answer: rad/s e) Suppose we want to change the circuit to have a peak time of 30 ms (0.03 s). What damped natural frequency would be required, in rad/s? Answer: rad/s
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