Ideal Spring
Figure 7.4 depicts the ideal spring.
From Hooke's law, we have that the applied force is proportional to the displacement of the spring:







The frequency response of the ideal spring, given the applied force as input and resulting velocity as output, is
In this case, the amplitude response grows


We call the compression velocity of the spring. In more
complicated configurations, the compression velocity is defined as the
difference between the velocity of the two spring endpoints, with positive
velocity corresponding to spring compression.
In circuit theory, the element analogous to the spring is the capacitor,
characterized by
, or
.
In an equivalent analog circuit, we can use the value
. The
inverse
of the spring stiffness is sometimes called the
compliance
of the spring.
Don't forget that the definition of impedance requires zero initial conditions for elements with ``memory'' (masses and springs). This means we can only use impedance descriptions for steady state analysis. For a complete analysis of a particular system, including the transient response, we must go back to full scale Laplace transform analysis.
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Series Combination of One-Ports
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Ideal Mass