Classical Dynamics of Particles and Systems
5th Edition
ISBN: 9780534408961
Author: Stephen T. Thornton, Jerry B. Marion
Publisher: Cengage Learning
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Textbook Question
Chapter 12, Problem 12.6P
Two identical harmonic oscillators are placed such that the two masses slide against one another, as in Figure 12-A. The frictional force provides a coupling of the motions proportional to the instantaneous relative velocity. Discuss the coupled oscillations of the system.
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Classical Dynamics of Particles and Systems
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- Show that, if a driven oscillator is only lightly damped and driven near resonance, the Q of the system is approximately Q2(TotalenergyEnergylossduringoneperiod)arrow_forwardObtain the response of a linear oscillator to a step function and to an impulse function (in the limit τ → 0) for overdamping. Sketch the response functions.arrow_forwardConsider a damped harmonic oscillator. After four cycles the amplitude of the oscillator has dropped to 1/e of its initial value. Find the ratio of the frequency of the damped oscillator to its natural frequency.arrow_forward
- Refer to the problem of the two coupled oscillators discussed in Section 12.2. Show that the total energy of the system is constant. (Calculate the kinetic energy of each of the particles and the potential energy stored in each of the three springs, and sum the results.) Notice that the kinetic and potential energy terms that have 12 as a coefficient depend on C1 and 2 but not on C2 or 2. Why is such a result to be expected?arrow_forwardAllow the motion in the preceding problem to take place in a resisting medium. After oscillating for 10 s, the maximum amplitude decreases to half the initial value. Calculate (a) the damping parameter β, (b) the frequency υ1 (compare with the undamped frequency υ0), and (c) the decrement of the motion.arrow_forwardIn the case of a damped pendulum, how would the dyanmics change as a fixed point varied from being a stable spiral, to a stable degenerate node, to a stable node? I know that all the trajectories continue to lose altitude, and that the pendulum goes from whirling clockwise over the top, loses energy, settles to a small oscillation, and eventually comes to rest at the bottom, but wasn't sure if this general description changes based on the variation of fixed points.arrow_forward
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