The motion of an oscillating system that is subject to damping. If the damping is proportional to the velocity of the body, then the equation of motion is:
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where x is the displacement of the body, m is its mass, k is the constant of proportionality of the restoring force (the ‘spring constant’) and µ is the damping constant. There are three distinct solutions of this second-order differential equation, depending on the constants involved:
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known as underdamping. The body oscillates, and the amplitude of the oscillation decreases exponentially with time.
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known as critical damping. The body returns to its equilibrium position at the optimum rate.
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known as overdamping. The body returns to its equilibrium position, but the excessive damping causes a slower return than in the critical case. |
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