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# 12 X1 T07 02 Simple Harmonic Motion

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### 12 X1 T07 02 Simple Harmonic Motion

1. 1. Simple Harmonic Motion
2. 2. Simple Harmonic Motion A particle that moves back and forward in such a way that its acceleration at any instant is directly proportional to its distance from a fixed point, is said to undergo Simple Harmonic Motion (SHM)
3. 3. Simple Harmonic Motion A particle that moves back and forward in such a way that its acceleration at any instant is directly proportional to its distance from a fixed point, is said to undergo Simple Harmonic Motion (SHM)
4. 4. Simple Harmonic Motion A particle that moves back and forward in such a way that its acceleration at any instant is directly proportional to its distance from a fixed point, is said to undergo Simple Harmonic Motion (SHM)
5. 5. Simple Harmonic Motion A particle that moves back and forward in such a way that its acceleration at any instant is directly proportional to its distance from a fixed point, is said to undergo Simple Harmonic Motion (SHM)
6. 6. Simple Harmonic Motion A particle that moves back and forward in such a way that its acceleration at any instant is directly proportional to its distance from a fixed point, is said to undergo Simple Harmonic Motion (SHM) (constant needs to be negative)
7. 7. Simple Harmonic Motion A particle that moves back and forward in such a way that its acceleration at any instant is directly proportional to its distance from a fixed point, is said to undergo Simple Harmonic Motion (SHM) (constant needs to be negative)
8. 8. Simple Harmonic Motion A particle that moves back and forward in such a way that its acceleration at any instant is directly proportional to its distance from a fixed point, is said to undergo Simple Harmonic Motion (SHM) (constant needs to be negative)
9. 9. Simple Harmonic Motion A particle that moves back and forward in such a way that its acceleration at any instant is directly proportional to its distance from a fixed point, is said to undergo Simple Harmonic Motion (SHM) (constant needs to be negative)
10. 10. when x = a , v = 0 ( a = amplitude)
11. 11. when x = a , v = 0 ( a = amplitude)
12. 12. when x = a , v = 0 ( a = amplitude)
13. 13. NOTE: when x = a , v = 0 ( a = amplitude)
14. 14. NOTE: when x = a , v = 0 ( a = amplitude)
15. 15. NOTE: when x = a , v = 0 ( a = amplitude)
16. 16. NOTE: Particle travels back and forward between x = - a and x = a when x = a , v = 0 ( a = amplitude)
17. 24. In general;
18. 25. In general;
19. 26. In general;
20. 27. In general;
21. 28. In general;
22. 29. In general;
23. 30. In general; the particle has;
24. 31. In general; the particle has;
25. 32. In general; the particle has; (time for one oscillation)
26. 33. In general; the particle has; (time for one oscillation) (number of oscillations per time period)
27. 34. e.g. ( i ) A particle, P, moves on the x axis according to the law x = 4sin3 t .
28. 35. e.g. ( i ) A particle, P, moves on the x axis according to the law x = 4sin3 t . a) Show that P is moving in SHM and state the period of motion.
29. 36. e.g. ( i ) A particle, P, moves on the x axis according to the law x = 4sin3 t . a) Show that P is moving in SHM and state the period of motion.
30. 37. e.g. ( i ) A particle, P, moves on the x axis according to the law x = 4sin3 t . a) Show that P is moving in SHM and state the period of motion.
31. 38. e.g. ( i ) A particle, P, moves on the x axis according to the law x = 4sin3 t . a) Show that P is moving in SHM and state the period of motion.
32. 39. e.g. ( i ) A particle, P, moves on the x axis according to the law x = 4sin3 t . a) Show that P is moving in SHM and state the period of motion.
33. 40. e.g. ( i ) A particle, P, moves on the x axis according to the law x = 4sin3 t . a) Show that P is moving in SHM and state the period of motion.
34. 41. e.g. ( i ) A particle, P, moves on the x axis according to the law x = 4sin3 t . a) Show that P is moving in SHM and state the period of motion. b) Find the interval in which the particle moves and determine the greatest speed.
35. 42. e.g. ( i ) A particle, P, moves on the x axis according to the law x = 4sin3 t . a) Show that P is moving in SHM and state the period of motion. b) Find the interval in which the particle moves and determine the greatest speed.
36. 43. ( ii ) A particle moves so that its acceleration is given by Initially the particle is 3cm to the right of O and traveling with a velocity of 6cm/s. Find the interval in which the particle moves and determine the greatest acceleration.
37. 44. ( ii ) A particle moves so that its acceleration is given by Initially the particle is 3cm to the right of O and traveling with a velocity of 6cm/s. Find the interval in which the particle moves and determine the greatest acceleration.
38. 45. ( ii ) A particle moves so that its acceleration is given by Initially the particle is 3cm to the right of O and traveling with a velocity of 6cm/s. Find the interval in which the particle moves and determine the greatest acceleration.
39. 46. ( ii ) A particle moves so that its acceleration is given by Initially the particle is 3cm to the right of O and traveling with a velocity of 6cm/s. Find the interval in which the particle moves and determine the greatest acceleration.
40. 47. ( ii ) A particle moves so that its acceleration is given by Initially the particle is 3cm to the right of O and traveling with a velocity of 6cm/s. Find the interval in which the particle moves and determine the greatest acceleration.
41. 48. ( ii ) A particle moves so that its acceleration is given by Initially the particle is 3cm to the right of O and traveling with a velocity of 6cm/s. Find the interval in which the particle moves and determine the greatest acceleration.
42. 49. ( ii ) A particle moves so that its acceleration is given by Initially the particle is 3cm to the right of O and traveling with a velocity of 6cm/s. Find the interval in which the particle moves and determine the greatest acceleration.
43. 50. ( ii ) A particle moves so that its acceleration is given by Initially the particle is 3cm to the right of O and traveling with a velocity of 6cm/s. Find the interval in which the particle moves and determine the greatest acceleration.
44. 51. NOTE:
45. 52. NOTE: At amplitude; v = 0 a is maximum
46. 53. NOTE: At amplitude; v = 0 a is maximum At centre; v is maximum a = 0
47. 54. Exercise 3D; 1, 6, 7, 10, 12, 14ab, 15ab, 18, 19, 22, 24, 25 (start with trig, prove SHM or are told) Exercise 3F; 1, 4, 5b, 6b, 8, 9a, 10a, 13, 14 a, b( ii,iv ), 16, 18, 19 (start with ) NOTE: At amplitude; v = 0 a is maximum At centre; v is maximum a = 0