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Obtaining the natural frequencies of linear time-invariant dynamic systems from driving-point system-function measurements employing conceptual source-measure units

This paper presents two mathematical conceptualizations of driving-point system-function measurement of linear time-invariant (LTI) systems with lumped-parameter description. Whereas the formalization of this dual pair of Source-Measure Units (SMU) has been - for the twin purposes of ease of demonstration and ready cognizance - effected with a specific relevance to electrical quantities, the underlying concept of system-function is sufficiently general to be universally applicable to all classes of LTI systems. The formulation has been done in the time-domain, thus retaining full immediacy with the real system variables. The outcome of the measurement, therefore, upon due rationalization, emerges as a rationic polynomial. The natural frequencies of the system are then extractible from the characteristic polynomial, which latter is contained in the measured rationic. The `naturality' of the system-under-test as observed from a specified port-of-access is thus laid bare. The method is illustrated through examples, which also show the invariance of the system characteristic polynomial with respect to the point of view of the observer, except in cases of pole-zero cancellation. An alternative interpretation of the singularities of the system-function has also been furnished.