VIBRATORY MOTION - An
oscillating motion; for example, that of the weight W, in Figure 1.
SIMPLE HARMONIC MOTION - A form of vibratory motion. The motion as a function of
the time is of the form X = a sin wt,
where a, w
are constants. The maximum displacement, a, from the mean position (X = 0) is
the amplitude; the frequency (rate at which motion repeats itself) is w/2p
cycles/sec, where has the dimensions of reciprocal time, e.g. reciprocal
seconds. The motion is also called harmonic or sinusoidal motion.
AMPLITUDE - Figure 2 shows a vibrating motion, which repeats itself every T
seconds. The maximum values of the displacement, x, from the reference position
(x = 0) are called amplitudes. These are (a1, a2. . .). The largest of these is
called the peak amplitude.
FREQUENCY - Rate at which
motion repeats itself per unit time. If the motion repeats itself every T
seconds, the frequency is 1/T cycles per second.
PERIOD, CYCLE The interval of time within which the motion repeats itself. In
Figure 2, this is T seconds. The term cycle tends to refer also to the sequence
of events within one period.
STEADY-STATE MOTION - A periodic motion of a mechanical system, e.g. a
continuously vibrating pendulum of constant amplitude.
TRANSIENT MOTION - A motion which changes with time in a non-periodic manner;
often the motion declines (attenuates) to a negligible value after a finite
period of time (e.g. impact effects which decay with time, etc.).
PERIODIC AND NON-PERIODIC MOTIONS - A motion, which repeats itself is periodic;
a motion, which does not repeat itself, is non-periodic.
HARMONICS - Any motion can be considered as made up of a series of simple
harmonic motions of different frequencies and amplitudes. The lowest-frequency
component is usually called the fundamental frequency; higher frequency
components are called harmonics or super-harmonics. Their frequencies are exact
multiples of the fundamental frequency. Sometimes, components of the frequencies
of which are a fraction of driving frequency are significant (e.g. the
"half-frequency" whirl of rotating shafts, etc.). Such components are
called subharmonics.
PULSE - Usually a displacement-time or force-time function describing an input
into a dynamical system.
PULSE SHAPE - The shape of the time-displacement or force-displacement curve of
a pulse. Typically, this might be a square wave, a rectangular pulse, or a half
sine-wave pulse. In general, however, the shape can be an arbitrary function of
the time.
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