Describe examples of damped oscillations. Solution In physics, damping is any ef

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Describe examples of damped oscillations.

Explanation / Answer

In physics, damping is any effect that tends to reduce the amplitude of oscillations in an oscillatory system, particularly the harmonic oscillator. In mechanics, friction is one such damping effect. For many purposes the frictional force Ff can be modeled as being proportional to the velocity v of the object: where c is the viscous damping coefficient, given in units of newton seconds per meter (N s/m) or simply kilograms per second. Generally, damped harmonic oscillators satisfy the second-order differential equation: where ?0 is the undamped angular frequency of the oscillator and ? is a constant called the damping ratio. The value of the damping ratio ? determines the behavior of the system. A damped harmonic oscillator can be: Overdamped (? > 1): The system returns (exponentially decays) to equilibrium without oscillating. Larger values of the damping ratio ? return to equilibrium slower. Critically damped (? = 1): The system returns to equilibrium as quickly as possible without oscillating. This is often desired for the damping of systems such as doors. Underdamped (0 < ? < 1): The system oscillates (at reduced frequency compared to the undamped case) with the amplitude gradually decreasing to zero. Undamped (? = 0): The system oscillates at its natural resonant frequency (?o).

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