1. 5.5 Modeling Harmonic Motion

2. 5.5 Modeling Harmonic Motion
We will do 5 problems on the handout you’ve received.
Groups will do 1 & 2 ... then we’ll do 3-5 as a class.

3. 5.5 Modeling Harmonic Motion
We will do 5 problems on the handout you’ve received.
Groups will do 1 & 2 ... then we’ll do 3-5 as a class.
Proverbs 3:5-6 Trust in the LORD with all your heart and
lean not on your own understanding; in all your ways
acknowledge him, and he will make your paths straight.

4. Frequency is defined as the reciprocal of
the period of a periodic function.

5. Frequency is defined as the reciprocal of
the period of a periodic function.
Problem 1 on your handout:

6. Frequency is defined as the reciprocal of
the period of a periodic function.
Problem 1 on your handout:
amp. : 5 inches
2π
per. : = 1 second
2π
freq.: 1 Hz.

7. Problem 2 on your handout:

8. Problem 2 on your handout:
a. amp. : .8
2π 2
per. : =
49π 49
49
freq. :
2

9. Problem 2 on your handout:
a. amp. : .8
2π 2
per. : =
49π 49
49
freq. :
2
b. increase a ... louder
decrease a ... quieter

10. Problem 2 on your handout:
a. amp. : .8
2π 2
per. : =
49π 49
49
freq. :
2
b. increase a ... louder
decrease a ... quieter
c. increase freq. ... sharp
decrease freq. ... flat

11. Problem 3 on your handout:

12. Problem 3 on your handout:
function: cosine

13. Problem 3 on your handout:
function: cosine
amp.: 6

14. Problem 3 on your handout:
function: cosine
amp.: 6
per.:

15. Problem 3 on your handout:
function: cosine
amp.: 6
normal period
per.: period =
b

16. Problem 3 on your handout:
function: cosine
amp.: 6
normal period
per.: period =
b
normal period
b=
period

17. Problem 3 on your handout:
function: cosine
amp.: 6
normal period
per.: period =
b
normal period
b=
period
2π
b=
1
4

18. Problem 3 on your handout:
function: cosine
amp.: 6
normal period
per.: period =
b
normal period
b=
period
2π
b=
1
4
b = 8π

19. Problem 3 on your handout:
function: cosine
amp.: 6
normal period
per.: period =
b
normal period
b=
period
2π
b=
1
4
b = 8π
y = 6 cos ( 8π t )

20. Problem 4 on your handout:

21. Problem 4 on your handout:
Let time = 0 be when the star is at it’s dimmest.

22. Problem 4 on your handout:
Let time = 0 be when the star is at it’s dimmest.
function:

23. Problem 4 on your handout:
Let time = 0 be when the star is at it’s dimmest.
function: -cosine

24. Problem 4 on your handout:
Let time = 0 be when the star is at it’s dimmest.
function: -cosine
amplitude:

25. Problem 4 on your handout:
Let time = 0 be when the star is at it’s dimmest.
function: -cosine
amplitude: .35

26. Problem 4 on your handout:
Let time = 0 be when the star is at it’s dimmest.
function: -cosine
amplitude: .35
period:

27. Problem 4 on your handout:
Let time = 0 be when the star is at it’s dimmest.
function: -cosine
amplitude: .35
2π
period: b=
5.2

28. Problem 4 on your handout:
Let time = 0 be when the star is at it’s dimmest.
function: -cosine
amplitude: .35
2π
period: b=
5.2
vertical shift:

29. Problem 4 on your handout:
Let time = 0 be when the star is at it’s dimmest.
function: -cosine
amplitude: .35
2π
period: b=
5.2
vertical shift: 4

30. Problem 4 on your handout:
Let time = 0 be when the star is at it’s dimmest.
function: -cosine
amplitude: .35
2π
period: b=
5.2
vertical shift: 4
⎛ 2π ⎞
y = −.35 cos ⎜ t ⎟ + 4
⎝ 5.2 ⎠

31. Problem 4 on your handout:
Let time = 0 be when the star is at it’s dimmest.
function: -cosine
amplitude: .35
2π please include when
period: b= t = 0 as other
5.2
equations are
vertical shift: 4 possible.
⎛ 2π ⎞
y = −.35 cos ⎜ t ⎟ + 4
⎝ 5.2 ⎠

32. Problem 5 on your handout:

33. Problem 5 on your handout:
function:

34. Problem 5 on your handout:
function: cosine

35. Problem 5 on your handout:
function: cosine
amplitude:

36. Problem 5 on your handout:
function: cosine
amplitude: 135

37. Problem 5 on your handout:
function: cosine
amplitude: 135
period:

38. Problem 5 on your handout:
function: cosine
amplitude: 135
1
period: frequency =
period

39. Problem 5 on your handout:
function: cosine
amplitude: 135
1
period: frequency =
period
b
frequency =
2π

40. Problem 5 on your handout:
function: cosine
amplitude: 135
1
period: frequency =
period
b
frequency =
2π
2π gfrequency = b

41. Problem 5 on your handout:
function: cosine
amplitude: 135
1
period: frequency =
period
b
frequency =
2π
2π gfrequency = b
b = 140π

42. Problem 5 on your handout:
function: cosine
amplitude: 135
1
period: frequency =
period
b
frequency =
2π
2π gfrequency = b
b = 140π
V = 135 cos (140π t )

43. HW #7
When you are not practicing, remember, someone
somewhere is practicing, and when you meet him
he will win. Ed Macauley