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Describe the motion of driven, or forced, damped harmonic motion. Write the equations of motion for forced, damped harmonic motion. In the real world, oscillations seldom follow true SHM. Friction of some sort usually acts to dampen the motion so it dies away, or needs more force to continue.
- 16.7: Damped Harmonic Motion
Explain critically damped system. A guitar string stops...
- 16.7: Damped Harmonic Motion
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. Although we can often make friction and other non-conservative forces negligibly small, completely undamped motion is rare.
Damped Harmonic Motion | Physics. 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)
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.
Eq.(4) is the desired equation of motion for harmonic motion with air drag. It models what is known as damped harmonic oscillations, and is more realistic than the case where b is assumed to be zero. It can thus be readily applied to most every-day oscillating systems provided they can be defined one-dimensionally.
The critically damped oscillator returns to equilibrium at X=0 in the smallest time possible without overshooting. Critical damping is often desired, because such a system returns to equilibrium rapidly and remains at equilibrium as well.
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 .
