<P> The figure also shows the time domain representation of the resulting vibration . This is done by performing an inverse Fourier Transform that converts frequency domain data to time domain . In practice, this is rarely done because the frequency spectrum provides all the necessary information . </P> <P> The frequency response function (FRF) does not necessarily have to be calculated from the knowledge of the mass, damping, and stiffness of the system--but can be measured experimentally . For example, if a known force over a range of frequencies is applied, and if the associated vibrations are measured, the frequency response function can be calculated, thereby characterizing the system . This technique is used in the field of experimental modal analysis to determine the vibration characteristics of a structure . </P> <P> The simple mass--spring damper model is the foundation of vibration analysis, but what about more complex systems? The mass--spring--damper model described above is called a single degree of freedom (SDOF) model since the mass is assumed to only move up and down . In more complex systems, the system must be discretized into more masses that move in more than one direction, adding degrees of freedom . The major concepts of multiple degrees of freedom (MDOF) can be understood by looking at just a 2 degree of freedom model as shown in the figure . </P> <P> The equations of motion of the 2DOF system are found to be: </P>

Distinguish between free vibration forced vibration and damped vibration