3521 Single DegreeofFreedom Structural Systems

Consider the lateral motion of the basic SDOF model, shown in Figure 35.2, consisting of a mass m, supported by springs with total linear elastic stiffness k, and a damper with linear viscosity c. This SDOF system is then subjected to an external disturbance characterized by f(t). The excited model responds with a lateral displacement x( t) relative to the ground that satisfies the equation of motion:

in which a superposed dot represents differentiation with respect to time. For a specified input, f(t), and with known structural parameters, the solution of this equation can be readily obtained.

In the above, f(t) represents an arbitrary environmental disturbance such as wind or an earthquake. In the case of an earthquake load

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