An SDF system with natural period and damping ratio ζ is subjected to the periodic force shown in Fig. P3.26 with an amplitude and period . (a) Expand the forcing function in its Fourier series. ...

An SDF system with natural period

and damping ratio ζ is subjected to the periodic force shown in Fig. P3.26 with an amplitude

and period
.

(a) Expand the forcing function in its Fourier series.

(b) Determine the steady-state response of an undamped system. For what values of

is the solution indeterminate?

(c) For
/
= 2, determine and plot the response to individual terms in the Fourier series. How many terms are necessary to obtain reasonable convergence of the series solution?