F t FI Fd Fs

in which FI, FD and FS are inertial, damping and spring (stiffness) forces, respectively. The inertial force is equivalent to the total acceleration of the mass M and can be written as M U when there is no base motion. If there is a base motion, the inertial force can be written as M (U + Ug). As is shown in figure3.2 U is the acceleration of the mass M relative to the base and Ugis the ground acceleration.The spring force can be written as Ku, which is a linear spring or linear stiffness. Other form of spring may be proposed which result in nonlinear equation. The damping force is viscous damping force and is given by FD = C U which C is the damping coefficient. This is a valid assumption when velocity is small. For high velocity, damping force is proportional to the square of the velocity. Thus the equation of the motion for a SDF system can be written as:

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