9780070109100, Chapter 18 3, Problem 4E

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Chapter 18.3, Problem 4E Step-by-step solution Step 1 of 4 4. (a) The first line of (18.21) is still valid, but its second line now becomes pt+1 pt = pt) + gj(pt Consequently, (18.23) becomes pt+1 - - - pt + jBUt = + j(a - T) And (18.24) becomes pt+1 - [2 - j(1 - g) - pt+1 + [1 - - - j)]pt = Step 2 of 4 (b) No, we still have p = m. Step 3 of 4 (c) With j = g = 1, we have a1 = - 2 and a2 = 1. Thus 4a2 iff 4 iff 4. The value of marks off the three cases from one another. Step 4 of 4 (d) With = 3, the roots are complex, with R = = 1; the path has stepped fluctuation and is With = 4, we have repeated roots, with b = 2) = -1; the time path has nonconvergent oscillation. With = 5, we have distinct real roots, b1, b2 = 1/2 ( 3 ± = -0.38, -2.62; the time path has divergent