is where and the phase angles f and u are, respectively, defined by sin f c1 A, cos f c2

Chapter 5, Problem 43

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is where and the phase angles f and u are, respectively, defined by sin f c1 A, cos f c2 A and , . (b) The solution in part (a) has the form x(t) xc(t) xp(t). Inspection shows that xc(t) is transient, and hence for large values of time, the solution is approximated by xp(t) g(g) sin(gt u), where . Although the amplitude g(g) of xp(t) is bounded as show that the maximum oscillations will occur at the value . What is the maximum value of g? The number is said to be the resonance frequency of the system. (c) When F0 2, m 1, and k 4, g becomes . Construct a table of the values of g1 and g(g1) corresponding to the damping coefficients b 2, b 1, , and . Use a graphing utility to obtain the graphs of g corresponding to these damping coefficients. Use the same coordinate axes. This family of graphs is called the resonance curve or frequency response curve of the system. What is g1 approaching as ? What is happening to the resonance curve as ? 44. Co