AN64 Answers: Chapter 8 17. (a) Simple harmonic (b) 8 m (c) 1 sec (d) 1 oscillation sec 19. (a) Simple harmonic (b) 9 m (c) 8 sec π (d) π 1 8 oscillation sec 21. (a) Simple harmonic (b) 7 m (c) 2 3 sec (d) 3 2 oscillations sec 23. y 1.25 t 2P 25. y 1.25 t P 27. y 3P x 2P y 5 x y 5 cos x 29. y 3P x 3P y 5 x y 5 2sin x 31. y 1.25 x 3P y 5 cos x y 5 sin x 33. y 2.5 x 3P y 5 sin x y 5 sin(2x) 35. (a) f x x x 1 2 cos cos 3 ( ) ( ) [ ] = − (b) y 1 x 2P cos x y 5 1 2 cos(3x) y 5 2 1 2 37. (a) G x x x 1 2 cos 6 cos 2 ( ) ( ) ( ) [ ] = + (b) y 1 x 2P cos(2x) y 5 1 2 cos(6x) y 5 1 2 39. (a) H x x x sin 4 sin 2 ( ) ( ) ( ) = + (b) y 2 x 2P y 5 sin(2x) y 5 sin(4x) 41. (a) d t e t 10 cos 4 25 0.49 2500 t 0.7 50 2π ( ) = − − ⎛ ⎝ ⎜⎜ ⎜ ⎞ ⎠ ⎟⎟ ⎟ − (b) 10 210 25 0 43. (a) d t e t 18 cos 4 0.36 3600 t 0.6 60 2π ( ) = − − ⎛ ⎝ ⎜⎜ ⎜ ⎞ ⎠ ⎟⎟ ⎟ − (b) 18 218 20 0 45. (a) d t e t 5 cos 4 9 0.64 400 t 0.8 20 2π ( ) = − − ⎛ ⎝ ⎜⎜ ⎜ ⎞ ⎠ ⎟⎟ ⎟ − (b) 5 25 15 0 47. (a) The motion is damped. The bob has mass m 20 kg = with a damping factor of 0.7 kg sec. (b) 20 m leftward (c) 20 220 25 0 (d) 18.33 m leftward (e) d 0 → 49. (a) The motion is damped. The bob has mass m 40 kg = with a damping factor of 0.6 kg sec. (b) 30 m leftward (c) 30 230 35 0 (d) 28.47 m leftward (e) d 0 → 51. (a) The motion is damped. The bob has mass m 15 kg = with a damping factor of 0.9 kg sec. (b) 15 m leftward (c) 15 215 30 0 (d) 12.53 m leftward (e) d 0 → 53. d t t 1040 ; 0.80 cos 1040 ω π π ( ) ( ) = = 55. d t t 880 ; 0.01 sin 880 ω π π ( ) ( ) = = 57. (a) V 1.25 t 3 (b) At t t 0, 2; = = at t t 1, 3 = = (c) During the approximate intervals t t 0.35 0.67, 1.29 1.75, < < < < and t 2.19 3 < ≤ 59. 24p 4p 21 6 61. 2.5 22.5 2 0 65. 1 20.3 5p 0 67. y x x 1 sin = 1 20.3 5p 0 y x x 1 sin 2 = 0.1 20.06 7p 0 y x x 1 sin 3 = 0.05 20.015 3p 0 69. f x x x 4 3 1 1( ) = − − − 70. xy x y log7 3 + ⎛ ⎝ ⎜⎜ ⎜ ⎞ ⎠ ⎟⎟ ⎟ 71. 4{ } 72. (a) 3 10 10 (b) 10 10 (c) 1 3 73. g f x x 10 5 ; Domain: , 3 5 ( ( ) ( ) = − −∞ ⎤ ⎦ ⎥ 74. 7 6 12 − 75. y x 3 2 11 2 = − + 76. e1 2 { } 77. 5, 8 [ ] − 78. 2, 3 5 ⎡ − ⎣ ⎢ ⎤ ⎦ ⎥
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