Answers to the Problems

Chapter 1

P1.1. a) x1 = 2 cos(40πt) + 0.7958 sin (40πt), x2 = −2 cos(40πt) + 2.387 sin(40πt) and x3 = 3 cos(40πt) + 3.979 sin(40πt) = 4.98 cos(40πt −0.925); hence, xmax = 4.98 cm and νmax = 6.26 m/s.

P1.2. a) images, where images, cos images and sin images.

P1.3. images, where images and images.

P1.4. a) F = −Kx, where K = 9π2m = 44.4 N/m. b) U(P) = 0.888 × 10−2 cos2(3πt) J, U(C) = 0.00888 sin2(3πt) J, U(T) = 0.00888 J. c) U(P) = 22.2 x2, U(C) = 0.00888 − 22.2 x2.

P1.5. F = −Kx; hence images.

P1.6. a) images, where K = K1 + K2. b) The lengths of the springs are: a = (K1/K)L1 + (K2/K)(LL2), b = (K2/K)L2 + (K1/K)(LL1) and ...

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