There are many oscillatory systems around us in our daily lives. Some of these oscillations are nuisances and should be stopped as quickly as possible.
For example, vehicles are actually inverted spring-mass systems. The body of a car (mass) sits on top of its suspension system (spring). Every time the car hits a bump, or drives over an uneven surface, the car goes into oscillation. Shock absorbers are designed to be critically damped so that the car returns to the equilibrium position in the shortest amount of time.
Buildings are also inverted pendulums. They may look rigid to our eyes, but they are actually elastic and bendable. They too can be set into dangerous oscillation by strong gusts of wind, or ground tremors. For this reason, skyscrapers are equipped with devices to damp these oscillations.
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Demonstrations