Free and Forced Vibrations

Every object that is disturbed -- struck, plucked, or otherwise set into motion and then left alone -- tends to oscillate at one particular frequency of its own, called its NATURAL FREQUENCY. When a simple pendulum is pulled aside and released, or a guitar string is plucked, the object performs FREE VIBRATIONS: it is given an initial displacement, the disturbing force is then withdrawn completely, and the body continues oscillating entirely on its own, at its own natural frequency, with NO further outside force keeping it going. In practice, a freely vibrating body continuously loses a little energy to frictional resistance from the surrounding medium (air resistance, internal damping, and so on), so its amplitude steadily shrinks over time until the vibrations eventually die out and the body comes to rest.

By contrast, in FORCED VIBRATIONS, a continuing EXTERNAL periodic force keeps acting on a body whose own natural period is generally different from the period of that external force -- the vibrations of a drill machine or a washing machine while running are both forced vibrations, as is a table-top vibrating because a tuning fork's stem is held pressed against it (and the table-top's vibration is different for tuning forks of different frequencies, since it is being FORCED to follow whichever fork's frequency is currently in contact with it). Here the body is made to vibrate at the frequency of the EXTERNAL force, not its own natural frequency, and the resulting amplitude of forced vibration depends on how close the forcing frequency is to the body's own natural frequency: the smaller this difference, the larger the amplitude, and vice versa. …