Figure 7.4 depicts the ideal spring.
The frequency response of the ideal spring, given the applied force as input and resulting velocity as output, isamplitude response grows dB per octave, and the phase shift is radians for all . Clearly, there is no such thing as an ideal spring which can produce arbitrarily large gain as frequency goes to infinity; there is always some mass in a real spring.
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.
Series Combination of One-Ports