An experimental sensitivity method for analyzing forced vibration data is developed and applied in this book. It is shown that if a set of measured mechanical system input-output functions is available in vibrating systems, an appropriate analytical linear parameterization of these functions leads to algebraic relationships between the measured data. These functions are solely a function of experimental frequency response function data and determine the linear forced response sensitivity to physical perturbations in the system mechanical properties. Applications in three key areas of mechanical dynamic systems are examined to verify and further study the requirements of the embedded sensitivity function approach in experimental sensitivity analysis. First, this technique is used to examine the forward problem of identifying optimal design modifications for reducing linear vibration resonance problems. Second, it is applied to characterize nonlinear mechanical systems and identify nonlinear input-output models for those systems. Third, it is applied to examine the inverse problem of identifying structural perturbations or damage.