The critically damped oscillator returns to equilibrium at X = 0 X = 0 size 12 a single time. As with critical damping, it too may overshoot the equilibrium position, but will reach equilibrium over a longer period of time.įigure 16.23 Displacement versus time for a critically damped harmonic oscillator (A) and an overdamped harmonic oscillator (B). Curve B in Figure 16.23 represents an overdamped system. Such a system is underdamped its displacement is represented by the curve in Figure 16.22. With less-than critical damping, the system will return to equilibrium faster but will overshoot and cross over one or more times. Critical damping is represented by Curve A in Figure 16.23. When we want to damp out oscillations, such as in the suspension of a car, we may want the system to return to equilibrium as quickly as possible Critical damping is defined as the condition in which the damping of an oscillator results in it returning as quickly as possible to its equilibrium position The critically damped system may overshoot the equilibrium position, but if it does, it will do so only once. Figure 16.23 shows the displacement of a harmonic oscillator for different amounts of damping. (The net force is smaller in both directions.) If there is very large damping, the system does not even oscillate-it slowly moves toward equilibrium. If you gradually increase the amount of damping in a system, the period and frequency begin to be affected, because damping opposes and hence slows the back and forth motion. Figure 16.22 In this graph of displacement versus time for a harmonic oscillator with a small amount of damping, the amplitude slowly decreases, but the period and frequency are nearly the same as if the system were completely undamped.
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