8. SIMPLE HARMONIC MOTION (SHM) (PART 1) Flashcards
1
Q
- What do we call any motion that repeats after a given period of time?
PROVIDE AN EXAMPLE.
A
- oscillatory motion
EG: the inner ear
: it works by transmitting sound-wave energy into a
series of vibrating bones
EG : waves
2
Q
- What is a massless spring characterised by?
A
- 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
3
Q
- What can be said about the magnitude of the force exerted by the spring on an object?
A
- it is proportional to the stretch of the spring
4
Q
- What does the “stretch” of the spring refer to?
A
- it refers to how far you have pulled the spring from its natural position
- NATURAL POSITION= EQUILIBRIUM POSITION
5
Q
- What is the force exerted by a spring on an object called?
A
- 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
6
Q
- Define Hooke’s Law.
A
- 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
7
Q
- How can Hooke’s Law be written in mathematical terms?
A
- F = -k . x
8
Q
- What do each of the components in the following formula represent:
F= -kx
A
- 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
9
Q
- What happens if you express F as F external in the equation: F= -kx
A
- this would now give you the external force needed to stretch the spring to a given amount (x)
10
Q
- F external is the negative of the restoring force (F).
What does this do to the equation?
A
- it removes the negative
- F= kx
- this is because the external force acts in the same direction as the displacement of the object
11
Q
- What does it mean when F external is positive?
A
- the material/ object is experiencing tension
12
Q
- What does it mean when F external is negative?
A
- the material/object is experiencing compression
13
Q
- What is simple harmonic motion?
A
- it is a type of periodic motion
- the restoring force is proportional to the displacement from the equilibrium position
( F ∝ x )
14
Q
- What is periodic motion?
A
- 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
15
Q
- What stops an Oscillation motion?
A
- Friction
16
Q
- What is each oscillation in oscillation motion called?
A
- a cycle
17
Q
- 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?
A
- it is called a period
- the symbol for it is T
18
Q
- What is frequency (f)?
A
- it has an SI unit called hertz (Hz)
- it is the number of cycles per second
19
Q
- How is frequency calculated?
A
- f = 1 / T
- T is the period of time (in seconds)
20
Q
- How is the period calculated?
A
- T= 1 / f
- f is the frequency in Hertz
21
Q
- What does a pendulum consist of?
A
- it consists of a mass hanging from a light cord
- this mass swings from side to side
22
Q
- What is the equilibrium point with regards to a pendulum?
A
- it is the point at which the pendulum is hanging straight down
23
Q
- Which force tends to restore the pendulum to its equilibrium point?
A
- gravity
24
Q
- With regards to working out the restoring force in a pendulum equation, what formula is used?
A
- F perpendicular ≈ - kx
- F perpendicular is the gravitational force on the object
25
25. How would we work out the spring constant of a pendulum?
Why do we work it out this way?
- 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
26
26. How would we work out the period of the pendulum?
- L is the length of the pendulum
- g= gravitational force
- π= constant (3.14)
27
27. What must you first investigate to understand the mechanical properties of different body components?
- you must investigate stress-strain relationships
28
28. What do we model to understand stress-strain relationships?
- we model nonlinear time-dependent properties
- we model time-dependent, viscoelastic properties
29
29. What are these models used for?
- they help to understand how bones can bend
- they help to understand the occurrence of fractures
30
30. What are the two mechanical classifications of body parts?
- passive
- active
31
31. What are passive components?
Give two examples.
- they are components which respond to outside forces
- EG: bones and tendons
32
32. What are active components?
Give an example.
- they generate forces
- muscles
33
33. Why is this division between active and passive components of the body not ideal?
- because muscles can act as both active elements and passive components
- it is dependent on the situation
34
34. What is the simplest type of passive response?
- harmonic
- Hookean behaviour
35
35. What are three characteristics of Hookean behaviour?
- 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
36
36. What are two examples of elastic media?
What does elastic media mean?
EG: bones
: tendons
Elastic media means that when a force is applied on the object, it will return back to its original position
37
37. In reality, is any material perfectly harmonic?
- no
38
38. Why do most materials deviate from perfectly harmonic behaviour?
- they experience large applied forces on them
- this causes deformations
39
39. What does the deformation of a material depend on?
- force
- stress
- it depends on them nonlinearly
40
40. Can deformations be reversible?
- yes they can
41
41. What happens to the elasticity of a material that has experiences a large stress?
- it is no longer elastic
- it undergoes plastic deformation
- it is irreversible
42
42. What does it mean when a material is irreversible?
- it never returns to the same size or shape when the stress is removed
- it can even fracture if the stresses become larger
43
43. Define elasticity.
- the property by which a body returns to its original size and shape
- it does this when the forces that deform it are removed
44
44. Define stress (σ) experienced within a solid?
- the magnitude of the force acting on the object (F)
- divided by the area (A) over which it acts
45
45. What is the formula for stress?
- σ = F/A
- stress = Force (N) / Area (m²)
46
46. What is the SI unit for stress?
- Pascals (Pa)
47
47. Define strain (ε)?
- it is the fractional deformation
- it results from a stress
48
48. How is strain measured?
- 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
49
49. What is the mathematical formula for strain?
- the SI unit for strain does not exist
- this is because strain is a ratio
50
50. What is Young's Modulus?
How else is this modulus called?
- it is the measure of the stress over the strain
- it can also be called the Modulus of elasticity
51
51. What is the mathematical formula for Young's modulus?
- Y = σ / ε
52
52. What does a large modulus mean?
- a large stress is required to produce a given strain
- the object is rigid
53
53. What characteristic of the object determines the value of Y (Young's Modulus)?
- the material of the object
54
54. What is Young's Modulus an important measure of?
- the mechanical behaviour of materials
- the larger the modulus, the tougher the material
55
55. What are isotropic materials?
- they are materials that have the same Young's Modulus in all directions
- it does not matter which direction you are stretching the object
56
56. What are Anisotropic materials?
- they are materials that have different Young's Moduli in different directions
- this is due to asymmetry in the microstructure of the material
