# RLC Circuits

Exactly like a [perfect] spring-and-mass simple harmonic oscillator, an LC circuit -- with no resistance -- would oscillate forever with constant amplitude. But there is always resistance! Including that resistance makes those oscillations damped oscillations -- exactly like 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 is present, the effect is to slow down the oscillation -- or make the frequency less.

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

If the oscillator -- either an RLC circuit or a mass-and-spring SHO -- goes through several oscillations we describe this by saying it is an underdamped harmonic 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 overdamping or as an overdamped oscillator.

This overdamping occurs 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 possible without overshooting or making an oscillation. Shock absorbers on automobile suspension systems and door closure mechanisms are examples of critically damped systems.

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(c) Doug Davis, 2002; all rights reserved