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Figure 15.6.4 shows the displacement of a harmonic oscillator for different amounts of damping. When the damping constant is small, b < 4mk− −−−√, the system oscillates while the amplitude of the motion decays exponentially. This system is said to be underdamped, as in curve (a).
- 16.7: Damped Harmonic Motion
Learning Objectives. By the end of this section, you will be...
- 16.7: Damped Harmonic Motion
Learning Objectives. By the end of this section, you will be able to: Compare and discuss underdamped and overdamped oscillating systems. Explain critically damped system. A guitar string stops oscillating a few seconds after being plucked. To keep a child happy on a swing, you must keep pushing.
Figure 3: Damped Harmonic Oscillator With the force of air drag (for suÿciently low velocities) given by Eq.(1) we can now analyze harmonic oscillator motion subject to a velocity dependent drag force.
Learning Objectives. By the end of this section, you will be able to: Compare and discuss underdamped and overdamped oscillating systems. Explain critically damped system. Figure 1. In order to counteract dampening forces, this dad needs to keep pushing the swing. (credit: Erik A. Johnson, Flickr)
122 16.7 Damped Harmonic Motion. Summary. Compare and discuss underdamped and overdamped oscillating systems. Explain critically damped system. Figure 1. In order to counteract dampening forces, this dad needs to keep pushing the swing. (credit: Erik A. Johnson, Flickr) A guitar string stops oscillating a few seconds after being plucked.
Damped Harmonic Motion: Illustrating the position against time of our object moving in simple harmonic motion. We see that for small damping, the amplitude of our motion slowly decreases over time. The simplest and most commonly seen case occurs when the frictional force is proportional to an object’s velocity.
When a damped oscillator is underdamped, it approaches zero faster than in the case of critical damping, but oscillates about that zero. The equation is that of an exponentially decaying sinusoid. The damping coefficient is less than the undamped resonant frequency .
