Inertial frequency period

A variation on PWM is pulse position modulation (PPM), also known as pulse period modulation or pulse frequency modulation (PFM). In this case, the duty-cycle pulse remains on for a fixed time while the base period is varied. The frequency of the pulses (how close together the pulses are) determines the voltage level. The neuromuscular system is an example of a pulse position modulation system. A muscle is made up of many discrete motor units. A motor unit has an all or nothing response to a nerve impulse in much the same way that a nerve impulse is a nonlinear (thresholded) all-or-nothing event. The level of sustained force output of a motor unit is dictated by the frequency of incidence of the nerve impulses, with the motor units dynamics [mechanical properties—inertial and damping properties (acts as a mechanical filter)] holding the force output smooth between incoming impulses. The motor unit is pulse frequency modulated by the nervous system. 

As pointed out in Chapter 1, the forces and displacements which are measured in a mechanical experiment are related to the states of stress and strain by the constitutive equation which describes the viscoelastic properties sought, as well as the equations of motion and continuity (equations 1 and 2 of Chapter 1). Ordinarily, there is considerable simplification because there is no change in density with time, and because gravitational forces can be neglected. In transient experiments (creep and stress relaxation), inertial forces can also be neglected by suitable restriction of the time scale, eliminating short times. In periodic (oscillatory) experiments, inertial forces may or may not play an important role depending on the frequency, sample dimensions, and mechanical consistency as described in Section D below. 

The other two instabilities shown in Fig. 28 may be observed only in liquid crystals (nematic, cholesteric, and smectic C). The first is the Carr-Helfrich instability, which is caused by a low-frequency electric field and occurs in the form of elongated vortices with their axis perpendicular to the original director alignment. The vortices cause a distortion of the director orientation, which is observed optically as a one-dimensional periodic pattern (Kapustin-Williams domains). The other anisotropic mode is observed only in highly conductive liquid crystals. For its interpretation the inertial term dvidt for the fluid velocity must be taken into account, which is why this mode may be called inertial mode. 

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