8. SIMPLE HARMONIC MOTION (SHM) (PART 1)

Question 1

1. What do we call any motion that repeats after a given period of time?

PROVIDE AN EXAMPLE.

Answer 1

• oscillatory motion

EG: the inner ear
: it works by transmitting sound-wave energy into a
series of vibrating bones

EG : waves

Question 2

2. What is a massless spring characterised by?

Answer 2

• it is characterised by the fact that the further you stretch it
• the harder it pulls back
• the more you compress a spring
• the harder it pushes back

Question 3

3. What can be said about the magnitude of the force exerted by the spring on an object?

Answer 3

• it is proportional to the stretch of the spring

Question 4

4. What does the “stretch” of the spring refer to?

Answer 4

• it refers to how far you have pulled the spring from its natural position
• NATURAL POSITION= EQUILIBRIUM POSITION

Question 5

5. What is the force exerted by a spring on an object called?

Answer 5

• the restoring force
• it brings the spring back to equilibrium
• it acts against the applied force
• it is proportional to the displacement of the spring

Question 6

6. Define Hooke’s Law.

Answer 6

• for spring (and any other elastic materials):
  - the magnitude of the restoring force is proportional
  to the displacement of the spring
  from its equilibrium position

Question 7

7. How can Hooke’s Law be written in mathematical terms?

Answer 7

• F = -k . x

Question 8

8. What do each of the components in the following formula represent:

F= -kx

Answer 8

• F= the magnitude of the force (restoring force)
• the negative sign (-)= means that the object is moving in
  the opposite direction from the force
  = the restoring force is always
  opposite of the displacement (x)
• k= the spring constant
  = it measures the spring stiffness
  = it is given in N/m
  = the ratio of the force applied to the resulting change in
  the length
• x = the distance from the equilibrium position

Question 9

9. What happens if you express F as F external in the equation: F= -kx

Answer 9

• this would now give you the external force needed to stretch the spring to a given amount (x)

Question 10

10. F external is the negative of the restoring force (F).
    What does this do to the equation?

Answer 10

• it removes the negative
• F= kx
• this is because the external force acts in the same direction as the displacement of the object

Question 11

11. What does it mean when F external is positive?

Answer 11

• the material/ object is experiencing tension

Question 12

12. What does it mean when F external is negative?

Answer 12

• the material/object is experiencing compression

Question 13

13. What is simple harmonic motion?

Answer 13

• it is a type of periodic motion
• the restoring force is proportional to the displacement from the equilibrium position
  ( F ∝ x )

Question 14

14. What is periodic motion?

Answer 14

• it is motion that is repeated in equal intervals of time
• the system doing the motion will then repeat itself
• it will then return to its initial position after the same amount of time

Question 15

15. What stops an Oscillation motion?

Answer 15

• Friction

Question 16

16. What is each oscillation in oscillation motion called?

Answer 16

• a cycle

Question 17

17. What is the time taken for the system to return to its initial state called?
    This is also known as the time taken to complete one full cycle of oscillation?

Answer 17

• it is called a period
• the symbol for it is T

Question 18

18. What is frequency (f)?

Answer 18

• it has an SI unit called hertz (Hz)
• it is the number of cycles per second

Question 19

19. How is frequency calculated?

Answer 19

• f = 1 / T
• T is the period of time (in seconds)

Question 20

20. How is the period calculated?

Answer 20

• T= 1 / f
• f is the frequency in Hertz

Question 21

21. What does a pendulum consist of?

Answer 21

• it consists of a mass hanging from a light cord
• this mass swings from side to side

Question 22

22. What is the equilibrium point with regards to a pendulum?

Answer 22

• it is the point at which the pendulum is hanging straight down

Question 23

23. Which force tends to restore the pendulum to its equilibrium point?

Answer 23

• gravity

Question 24

24. With regards to working out the restoring force in a pendulum equation, what formula is used?

Answer 24

• F perpendicular ≈ - kx
• F perpendicular is the gravitational force on the object

Question 25

25. How would we work out the spring constant of a pendulum?

Why do we work it out this way?

Answer 25

• k = mg / L
• k = spring constant
• mg = gravitational force of the object
• L= length of the cord
• we work it out this way because there is no spring present

Question 26

26. How would we work out the period of the pendulum?

Answer 26

• L is the length of the pendulum
• g= gravitational force
• π= constant (3.14)

Question 27

27. What must you first investigate to understand the mechanical properties of different body components?

Answer 27

• you must investigate stress-strain relationships

Question 28

28. What do we model to understand stress-strain relationships?

Answer 28

• we model nonlinear time-dependent properties
• we model time-dependent, viscoelastic properties

Question 29

29. What are these models used for?

Answer 29

• they help to understand how bones can bend
• they help to understand the occurrence of fractures

Question 30

30. What are the two mechanical classifications of body parts?

Answer 30

• passive
• active

Question 31

31. What are passive components?
    Give two examples.

Answer 31

• they are components which respond to outside forces
• EG: bones and tendons

Question 32

32. What are active components?
    Give an example.

Answer 32

• they generate forces
• muscles

Question 33

33. Why is this division between active and passive components of the body not ideal?

Answer 33

• because muscles can act as both active elements and passive components
• it is dependent on the situation

Question 34

34. What is the simplest type of passive response?

Answer 34

• harmonic
• Hookean behaviour

Question 35

35. What are three characteristics of Hookean behaviour?

Answer 35

• the deformations are linear with the applied force and the stresses
• the response is independent of time
• all potential energy is stored in media that it can be extracted from

Question 36

36. What are two examples of elastic media?
    What does elastic media mean?

Answer 36

EG: bones
: tendons

Elastic media means that when a force is applied on the object, it will return back to its original position

Question 37

37. In reality, is any material perfectly harmonic?

Answer 37

• no

Question 38

38. Why do most materials deviate from perfectly harmonic behaviour?

Answer 38

• they experience large applied forces on them
• this causes deformations

Question 39

39. What does the deformation of a material depend on?

Answer 39

• force
• stress
• it depends on them nonlinearly

Question 40

40. Can deformations be reversible?

Answer 40

• yes they can

Question 41

41. What happens to the elasticity of a material that has experiences a large stress?

Answer 41

• it is no longer elastic
• it undergoes plastic deformation
• it is irreversible

Question 42

42. What does it mean when a material is irreversible?

Answer 42

• it never returns to the same size or shape when the stress is removed
• it can even fracture if the stresses become larger

Question 43

43. Define elasticity.

Answer 43

• the property by which a body returns to its original size and shape
• it does this when the forces that deform it are removed

Question 44

44. Define stress (σ) experienced within a solid?

Answer 44

• the magnitude of the force acting on the object (F)
• divided by the area (A) over which it acts

Question 45

45. What is the formula for stress?

Answer 45

• σ = F/A
• stress = Force (N) / Area (m²)

Question 46

46. What is the SI unit for stress?

Answer 46

• Pascals (Pa)

Question 47

47. Define strain (ε)?

Answer 47

• it is the fractional deformation
• it results from a stress

Question 48

48. How is strain measured?

Answer 48

• it is measured as a ratio
• it is the ratio between:
  • change in the dimension of the body
  • and the original dimension in which the change
    occurred

Question 49

49. What is the mathematical formula for strain?

Answer 49

• the SI unit for strain does not exist
• this is because strain is a ratio

Question 50

50. What is Young’s Modulus?
    How else is this modulus called?

Answer 50

• it is the measure of the stress over the strain
• it can also be called the Modulus of elasticity

Question 51

51. What is the mathematical formula for Young’s modulus?

Answer 51

• Y = σ / ε

Question 52

52. What does a large modulus mean?

Answer 52

• a large stress is required to produce a given strain
• the object is rigid

Question 53

53. What characteristic of the object determines the value of Y (Young’s Modulus)?

Answer 53

• the material of the object

Question 54

54. What is Young’s Modulus an important measure of?

Answer 54

• the mechanical behaviour of materials
• the larger the modulus, the tougher the material

Question 55

55. What are isotropic materials?

Answer 55

• they are materials that have the same Young’s Modulus in all directions
• it does not matter which direction you are stretching the object

Question 56

56. What are Anisotropic materials?

Answer 56

• they are materials that have different Young’s Moduli in different directions
• this is due to asymmetry in the microstructure of the material