Orthogonal functions can be integrated using a so-called operational matrix. This characteristic transforms a set of second order differential equations into algebraic equations which are easily solved. In the case of mechanical systems the unknown parameters can be determined from these algebraic equations. For this purpose, the input and output signals have to be expanded in time orthogonal functions. This technique can be also applied for sensitivity analysis. In this paper Fourier series, Legendre polynomials, Jacobi polynomials, Chebyshev series, Block-Pulse functions and Walsh functions are used to expand the signals as time functions.