Provide a detailed discussion of the amplitude curves shown in Figure 11.12. Discuss the variation of the amplitude as a sweep is made of the frequency from small values to larger values.

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Co F=0. B=0 6 2 [Col A 6 4 2 =01 F=0 Locus of tangency points 200 300 w (a) 0.5 an (b) e--0.1 1.50% Figure 11.12: Amplitude curves Col vs. w, for the Duff- ing equation for two values of s3, with multiple values of sF. In (a), the dotted lines for 3 = 0 represent the linear response. The dotted lines that slant to the right represent the nonlinear case for F = 0 as well as the lo- cus of tangency points. Two tangent lines are drawn. In (b), the curves slant to the left because of the negative parameter 8.