Inductance

RLC CircuitsExactly like a [perfect] spring-and-mass simple harmonic oscillator, an LC circuit -- with

noresistance-- would oscillate forever with constant amplitude. But there is always resistance! Including that resistance makes those oscillationsdampedoscillations --exactlylike friction in a spring-and-mass simple harmonic oscillator.The "natural frequency" or "resonant frequency" of an undamped spring-and-mass simple harmonic oscillator is

when no fricition is present.

When friction

ispresent, the effect is toslow downthe oscillation -- or make the frequency less.

In exactly the same manner, when there is resistance in an LC circuit -- so it becomes anRLCcircuit -- the frequency of oscillation becomes smaller.If the oscillator -- either an RLC circuit

ora mass-and-spring SHO -- goes through several oscillations we describe this by saying it is anunderdampedharmonic oscillator.If the damping is great enough -- that is, if the resistance R is large enough -- it will not go through a complete oscillation at all. This is known as

overdampingor as anoverdampedoscillator.This

overdampingoccurs for R > SQRT(4L/C).The special case of R = SQRT(4L/C) is known as

critical damping. A critically damped oscillator damps out the oscillations as quickly as possiblewithoutovershooting or making an oscillation. Shock absorbers on automobile suspension systems and door closure mechanisms are examples of critically damped systems.

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