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By John G. Webster (Editor)

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**Example text**

In periodic vibrations, the motion of an object repeats itself in an oscillatory manner. This can be represented by a sinusoidal waveform x(t) = Xpeak sin(ωt) u(t) = dx/dt = ωXpeak cos(ωt) = Upeak sin(ωt + π/2) This section is concerned with applications of accelerometers to measure physical properties such as acceleration, vibration and shock, and motions associated with inertial navigation. A full understanding of accelerometer dynamics is necessary in relation to characteristics of acceleration, vibration, and (39) where u(t) is the time-dependent velocity, and Upeak ϭ ͶXpeak is the maximum velocity.

Ratio the particle velocity: Zs = p u (8) The unit is the rayl, equal to Pa и s и mϪ1. The third type of impedance, called the mechanical impedance, Zm, is defined as the quotient of the force exerted on a given area and the resulting particle velocity: Zm = pS u (9) The unit of Zm is the mechanical ohm, equal to N и s/m. Each type of impedance has certain advantages in the solution of specific problems. For instance: the acoustic impedance does not vary with changes in cross section of a conduit down which a sound wave is traveling; specific acoustic impedance in a plane progressive wave is nearly the same at all points; mechanical impedance may be used directly in equivalent circuits.

In this case, the statistical properties of vibrations vary in time. Methods such as (42) where f(t) is the force, m the mass, c the velocity constant, and k the spring constant. Nevertheless, in seismic accelerometers the base of the arrangement is in motion too. Therefore, Eq. (42) may be generalized by taking the effect motion of the base into account. Then this equation may be modified as m d 2 z/dt 2 + c dz/dt + kz = mg cos(θ ) − m d 2 x1 /dt 2 (43) where z ϭ x2 Ϫ x1 is the relative motion between the mass and the base, x1 the displacement of the base, x2 the displacement of the mass, and the angle between the sense axis and gravity.

### 30.Instrumentation and Measurement by John G. Webster (Editor)

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