Simple Harmonic Motion
Simple Harmonic Motion A particle that moves back and forward in such a way that its acceleration at any instant is direct...
Simple Harmonic Motion A particle that moves back and forward in such a way that its acceleration at any instant is direct...
Simple Harmonic Motion A particle that moves back and forward in such a way that its acceleration at any instant is direct...
Simple Harmonic Motion A particle that moves back and forward in such a way that its acceleration at any instant is direct...
Simple Harmonic Motion A particle that moves back and forward in such a way that its acceleration at any instant is direct...
Simple Harmonic Motion A particle that moves back and forward in such a way that its acceleration at any instant is direct...
Simple Harmonic Motion A particle that moves back and forward in such a way that its acceleration at any instant is direct...
Simple Harmonic Motion A particle that moves back and forward in such a way that its acceleration at any instant is direct...
when  x  =  a  ,  v  = 0 ( a  = amplitude)
when  x  =  a  ,  v  = 0 ( a  = amplitude)
when  x  =  a  ,  v  = 0 ( a  = amplitude)
NOTE: when  x  =  a  ,  v  = 0 ( a  = amplitude)
NOTE: when  x  =  a  ,  v  = 0 ( a  = amplitude)
NOTE: when  x  =  a  ,  v  = 0 ( a  = amplitude)
NOTE: Particle travels back and forward between  x  = - a  and  x  =  a when  x  =  a  ,  v  = 0 ( a  = amplitude)
 
 
 
 
 
 
 
In general;
In general;
In general;
In general;
In general;
In general;
In general; the particle has;
In general; the particle has;
In general; the particle has; (time for one oscillation)
In general; the particle has; (time for one oscillation) (number of oscillations  per time period)
e.g. ( i ) A particle,  P,  moves on the  x  axis according to the law  x  = 4sin3 t .
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 a...
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 a...
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 a...
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 a...
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 a...
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 a...
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 a...
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 a...
( ii ) A particle moves so that its acceleration is given by Initially the particle is 3cm to the right of  O  and traveli...
( ii ) A particle moves so that its acceleration is given by Initially the particle is 3cm to the right of  O  and traveli...
( ii ) A particle moves so that its acceleration is given by Initially the particle is 3cm to the right of  O  and traveli...
( ii ) A particle moves so that its acceleration is given by Initially the particle is 3cm to the right of  O  and traveli...
( ii ) A particle moves so that its acceleration is given by Initially the particle is 3cm to the right of  O  and traveli...
( ii ) A particle moves so that its acceleration is given by Initially the particle is 3cm to the right of  O  and traveli...
( ii ) A particle moves so that its acceleration is given by Initially the particle is 3cm to the right of  O  and traveli...
( ii ) A particle moves so that its acceleration is given by Initially the particle is 3cm to the right of  O  and traveli...
NOTE:
NOTE: At amplitude; v  = 0 a  is maximum
NOTE: At amplitude; v  = 0 a  is maximum At centre; v  is maximum a  = 0
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, 5...
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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
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