Technical Mathematics, Sixth Edition

D.15. CHAPTER 15

Exercise 1

1. amplitude = 2; period = 360°; phase shift = 0°

3. amplitude = 1; period = 180°; phase shift = 0°

5. amplitude = 3; period = 180°; phase shift = 0°

7. amplitude = 1; period = 360°; phase shift = −15°

9. amplitude = 1; period = 2π; phase shift = π/2

11. amplitude = 3; period = 360°; phase shift = −45°

13. amplitude = 4; period = 2π; phase shift = π/4

15. amplitude = 1; period = 180°; phase shift = −27.5°

17. amplitude = 1; period = 2π/3; phase shift = π/9

19. amplitude = 3; period = 180°; phase shift = −27.5°

21. amplitude = 2; period = 2π/3; phase shift = π/6

23. amplitude = 3.73; period = 83.3°; phase shift = −12.8°

25. zeros at x = 82.5° and 172.5°; y = 0.7071 at x = 15°

27. zeros at x = 1 and 2.05; y = 0 at x = 1

33. r sin(θ+38.6°)

Exercise 2

Exercise 3

1. P = 0.0147 s; ω = 427 rad/s

3. P = 0.0002 s; ω = 31,400 rad/s

5. f = 8 Hz; ω = 50.3 rad/s

7. 3.33 s

9. P = 0.0138 s; f = 72.4 Hz

11. P = 0.0126 s; f = 79.6 Hz

13. P = 400 ms; amplitude = 10; φ = 1.1 rad

15. y = 5 sin (750t + 15°)

23. V_max = 4.27 V; P = 13.6 ms; f = 73.7 Hz; φ = 27° = 0.471 rad; V(0.12) = −2.11 V

25. i = ...