tutorial_damped_harmonic_motion

tutorial_damped_harmonic_motion - Pretest: Damped harmonic...

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Pretest: Damped harmonic motion: Motion graphs Name ©2008 Physics Department, Grand Valley State University, Allendale, MI. The x vs. t graph below represents the motion of a simple harmonic oscillator that is released from rest at t = 0. A. On the graph, clearly label these features of the motion: amplitude period B. In answering parts i and ii below, imagine that a retarding force is applied to the oscillator, causing it to become underdamped ( i.e., it is not a simple harmonic oscillator anymore). i. On the graph above, sketch a qualitatively correct x vs. t graph that could represent the motion of the underdamped oscillator if it were released from rest at the same initial position as before. In the space below, explain how you decided to draw the graph the way you did. ii. Consider the motion of the (underdamped!) oscillator as it first passes through the location x = 0. Which statement below (circle one) best describes the motion of the oscillator when it passes through x = 0? In the space below, explain the reasoning for your choice. The oscillator is speeding up as it passes through x = 0. The oscillator is slowing down as it passes through x = 0. The oscillator has attained a maximum speed (and is therefore neither speeding up nor slowing down) as it passes through x = 0. x(t) t
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©2008 Physics Department, Grand Valley State University, Allendale, MI. I. Displacement versus time Consider a simple harmonic oscillator ( e.g., a mass connected to an ideal spring) that experiences a retarding force that is always proportional to the speed of the oscillator. At t = 0 the oscillator is displaced 1.0 m away from equilibrium and released from rest. The displacement versus time (x vs. t) graph at right represents the subsequent motion of the oscillator. (Because the motion still exhibits oscillatory behavior, the oscillator is said to be underdamped ). A. According to the graph, how (if at all) does each of the following quantities change as time elapses? the maximum displacement attained with each oscillation the period of oscillation B. Suppose that the retarding force were removed ( e.g., the oscillator is now immersed in a vacuum rather than air). Imagine that the oscillator is now released with the same initial conditions as before. How, if at all, would removing the retarding force affect each of the following quantities? Discuss your reasoning with your partners.
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tutorial_damped_harmonic_motion - Pretest: Damped harmonic...

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