A machine is loaded by a periodic "sawtooth" shaped force, as depicted in Figure 3.61. The load is assumed to have existed for a very long time. Model this force using:

(a) a one-term Fourier series,

(b) a three-term Fourier series, and

(c) a five-term Fourier series. In each case solve for the response as a function of time. System properties are \(m=1 \mathrm{~kg}\), \(k=9 \mathrm{~N} / \mathrm{cm}, \zeta=0.15, T=1 \mathrm{~s}\), and \(A=1 \mathrm{~cm}\).

Transcribed Image Text:

F(t) T Figure 3.61: Sawtooth loading. F(0) /2 10 I 3/2 2 Figure 3.62: Triangle forcing function.