Reading Assignment 3 Damped and Driven Oscillators

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11/4/23, 4:24 PM Reading Assignment 3: Damped and Driven Oscillators: Attempt review Started on Saturday, 19 September 2020, 9:46 PM State Finished Completed on Monday, 21 September 2020, 12:21 AM Time taken 1 day 2 hours Marks 4.00/4.00 Grade 100.00 out of 100.00 Question 1 Correct Mark 1.00 out of 1.00 A mass-spring system has a damping force of bz which opposes the velocity of the mass, m. If the spring constant is k and the angular frequency of the undamped system is wq which of the following are valid expressions for the damping ratio, (, of the system. Important: More than one answer may be correct. Select all correct answers and no incorrect answers to obtain full marks. Select all that apply: b Cross out ¢ 2./mk b Cross out b 2muw, mw bk cross out Wo b/ £ cross out m b cross out 2mk b cross out 2mk Your answer is correct. The damping ration for a mass-spring system is defined as: b 2/mk The correct answers are: b ' 2muw, Marks for this submission: 1.00/1.00. https://eclass.srv.ualberta.ca/mod/quiz/review.php?attempt=5741061&cmid=4375315 1/4

11/4/23, 4:24 PM Reading Assignment 3: Damped and Driven Oscillators: Attempt review Question 2 Correct Mark 2.00 out of 2.00 For the following systems described below say whether each one is either over damped, under damped or critically damped. In all cases wy refers to the natural oscillation frequency of the undamped system, ( is the damping ratio and A and B are constants. The displacement of the system is given by (A + Bt)e 0!, critically damped v under damped v The system oscillates back and forth but with an exponentially decreasing amplitude. over damped v The displacement of the system is given by Ae%! + Be%! where both ¢, and g_ are real and less than zero. A system with { < 1 under damped v A system which has its damping tuned so that it returns to its equilibrium position, and stays there, in the fastest critically damped possible time. v The correct answer is: The displacement of the system is given by (A + Bt)e™“*. — critically damped, The system oscillates back and forth but with an exponentially decreasing amplitude. = under damped, The displacement of the system is given by Ae%+* + Bed-* where both g, and g_ are real and less than zero. — over damped, A system with ( < 1 — under damped, A system which has its damping tuned so that it returns to its equilibrium position, and stays there, in the fastest possible time. — critically damped Marks for this submission: 2.00/2.00. https://eclass.srv.ualberta.ca/mod/quiz/review.php?attempt=5741061&cmid=4375315 2/4

11/4/23, 4:24 PM Reading Assignment 3: Damped and Driven Oscillators: Attempt review Question 3 Correct Mark 1.00 out of 1.00 Looking at the solution derived for a driven harmonic oscillator a long time after the system is set in motion which one of the following statements is true? Select one: The oscillator vibrates at the driving frequency and not cross out & Correct, well at the natural frequency of the system. The oscillator vibrates at the natural frequency of the system regardless of the driving frequency. The oscillator vibrates at a frequency somewhere between the driving frequency and the natural frequency of the system. The oscillator vibrates with a changing frequency which moves back and forth between the natural frequency and the driving frequency. The oscillator does not vibrate: the driving frequency cancels out the natural vibrations of the system so that there is no movement. Your answer is correct. The correct answer is: The oscillator vibrates at the driving frequency and not at the natural frequency of the system. Marks for this submission: 1.00/1.00. Question 4 Complete Not graded Which topics or concepts in this part of oscillations did you have the most trouble understanding? [Answering this question is optional and does not count towards your assignment mark.] done! Cross out Ccross out Ccross out Ccross out p The Driven Oscillators. N https://eclass.srv.ualberta.ca/mod/quiz/review.php?attempt=5741061&cmid=4375315 3/4

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11/4/23, 4:24 PM Reading Assighment 3: Damped and Driven Oscillators: Attempt review https://eclass.srv.ualberta.ca/mod/quiz/review.php?attempt=5741061&cmid=4375315 4/4