22BsolnsHW7 - Math 22B Solutions Homework 7 Spring 2008...

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Math 22B Solutions Homework 7 Spring 2008 Section 3.9 17. Solution (a) u 00 + . 25 u 0 + 2 u = 2 cos ωt From equation (1) in section 3.9, m = 1, γ = . 25, k = 2, F 0 = 2, ω 2 0 = 2. From (5) in 3.9, Δ = q (2 - ω 2 ) 2 + ω 2 16 = . 25 64 - 63 ω 2 + 16 ω 4 . So tan δ = ω 4(2 - ω 2 ) . (b) R = F 0 Δ = 2 . 25 64 - 63 ω 2 +16 ω 4 = 8 64 - 63 ω 2 +16 ω 4 . (c) See figure 1 (d) A is maximum when the denominator of R is minumum, that is, when ω = ω max = 3 14 8 1 . 4. Section 7.2 20. Solution Suppose A is nonsingular, and that there exists matrices B and C such that AB = I and AC = I . Then A ( B - C ) = AY = 0 nxn . We write the difference of two matrices,
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