The analysis of the Fourier Transform Mechanical Spectroscopy (FTMS) method in application to measuring viscoelastic properties of a material in a linear viscoelastic domain shows that sensitivity of the method at higher harmonics strongly depends on the form of the input signal. Then the problem of the choice of the optimal signal is discussed. It is shown that the function f(t)=(sinomegat)/t provides the best form of the input signal basing on the requirement to hold equal amplitudes of all higher harmonics. The comparison of data obtained by the FTMS method and viscoelastic properties measured in harmonic oscillations demonstrates that both methods give adequate results. The application of the FTMS method with the input signal of the optimal form for measuring linear viscoelastic properties of a material saves time of an experiment (up to 3-4 times) and might be specially interesting for analysis of unstable ("rheokinetic") materials, in particular, curing oligomers, because the time evolution of different relaxation modes can proceed in different manner.