2.1 A rather heavy compression spring weighing 1.0 lb has a stiffness k _s of 2000 lb/in. To the casual observer it looks like a spring but feels like a mass. This problem deals with the choice of a suitable lumped-parameter model for such a spring.

According to vibration theory, this spring, containing both mass and stiffness itself, will respond with different kinds of oscillations, depending on how it is forced (i.e., its boundary conditions). ^[4] This means that the choice of an approximate lumped-parameter model for this element will depend partly on the elements with which it interacts and partly on the range of frequencies, or rate of variation, of inputs applied to the system containing it. Obviously, in a simple system containing this heavy spring and an attached mass, the spring may be modeled to a good degree of approximation as a pure spring if the attached mass is at least an order of magnitude greater than the self-mass of the spring and if the portion of the force applied to the spring required for accelerating its self-mass is small compared with the force required for deflecting the spring. Likewise, the spring might be approximately modeled as a pure mass if it interacts with another spring having a stiffness at least an order of magnitude smaller than its own stiffness and if its self-deflection is small compared with the deflection of the other spring as a result of the acceleration force of its mass.