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Critical damping viewed as the minimum value of damping that prevents oscillation is a desirable solution to many vibration problems. Increased damping implies more energy dissipation, and more phase lag in the response of a system. Reduced damping means more oscillation, which is often undesirable.
The damping may be quite small, but eventually the mass comes to rest. If the damping constant is \(b = \sqrt{4mk}\), the system is said to be critically damped, as in curve (\(b\)). An example of a critically damped system is the shock absorbers in a car. It is advantageous to have the oscillations decay as fast as possible.
Damping is a frictional force, so it generates heat and dissipates energy. When the damping constant b is small we would expect the system to still oscillate, but with decreasing amplitude as its energy is converted to heat. Over time it should come to rest at equilibrium. This is exactly what we see in (3).
Critically Damped: “The condition in which the damping of an oscillator causes it to return as quickly as possible to its equilibrium position without oscillating back and forth about this position.
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.
Framing Question. How do we model oscillatory phenomena in which air drag causes a decrease in oscillation amplitude? 1.1 Drag and general Damping Forces. To achieve our objective of finding a more accurate model for oscillatory phenomena, we need to first find the correct Newton’s second law equation for such systems.
14 Ιουλ 2024 · Critically Damped Vibrations: In a critically damped system, the damping is precisely the amount needed to prevent oscillations. The system returns to equilibrium as quickly as possible without oscillating. This type of damping is ideal for applications where quick stabilization is required, such as in automotive shock absorbers.
