Brainscape's Knowledge GenomeTM

Browse over 1 million classes created by top students, professors, publishers, and experts.


See full index

Biophysics LAB 1ST SEM > 6. Resonance > Flashcards

6. Resonance Flashcards

1
Q

What is elasticity?

A

a solid body is called elastic, if upon deformation by external forces such forces emerge in the body that tend to restore its original shape.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
2
Q

what is elastic deformation?

A

The spring constant can be calculated from t the change of the external force 􏰂acting on the body and the deformation􏰂

  • ∆Fext is the the change of the external force
  • ∆x is the deformation
  • k is the spring constant.
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
3
Q

What is Hook’s law formula?

A

F 􏲣 􏲏= -k x
F is the (pulling, pressing, bending etc.) restoring force emerging in the body
x is the deformation,
k is the spring constant

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
4
Q

What do vibration, swinging, or oscillation refer to?

A

a repeating motion, variation, displacement around the equilibrium value of a physical, chemical, or biochemical variable.
-> a phenomenon where a quantity varies in time about an equilibrium value.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
5
Q

What is SIMPLE HARMONIC OSCILLATION?

A

An oscillation is harmonic, if the temporal change of the variable is sinusoidal.

→ Such oscillation forms if the restoring force bringing the system back to equilibrium is proportional to the displacement and directed towards the equilibrium position.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
6
Q

Simple harmonic oscillation can be related to uniform ___ motion

A

circular

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
7
Q

The motion of a point-like object is called simple harmonic oscillation, if the restoring force, which drives the motion back towards the equilibrium position, is directly proportional to the displacement → The time dependence of the displacement is_____

A

Sinusoidal

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
8
Q

Simple harmonic oscillation can be related to uniform circular motion.

→ Consider a point rotating along a circle of radius R with constant angular velocity 􏰑 (Fig. 2).

→ The vertical projection of the rotating point on a straight line is a simple harmonic motion ___, such as the motion of mass m on a spring displaced from its equilibrium position

A

up and down

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
9
Q

What is AMPLITUDE?

A

the maximum displacement of an oscillation from the equilibrium position (within a period).

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
10
Q

Simple harmonic oscillation can be related to uniform circular motion.

→ Consider a point rotating along a circle of radius R with constant angular velocity 􏰑 (Fig. 2). The vertical projection of the rotating point on a straight line is a simple harmonic motion up and down, such as the motion of mass m on a spring displaced from its equilibrium position (Fig. 2, states a - f ).

→ In this case the maximum displacement, i.e., the amplitude of the oscillation is: ___

A

A = R.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
11
Q

Simple harmonic oscillation is characterized by __ (2 things)

A
  • the eigenfrequency f0 (also called natural frequency)
  • the time period T = 1/f0.
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
12
Q

What is EIGENFREQUENCY, NATURAL FREQUENCY?

A
  • the frequency at which a free oscillatory system oscillates.
  • Eigenfrequency is independent of the displacement; its value is defined only by the characteristics of the system.
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
13
Q

SIMPLE HARMONIC OSCILLATION

The periodic displacements during the oscillation are accompanied by the ___

A

Interconversion of different forms of energy characteristic for the oscillatory system

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
14
Q

SIMPLE HARMONIC OSCILLATION

. In an ideal oscillatory system (i.e., those working without loss of energy), the sum of these energies is __

A

Sinusoidal

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
15
Q

In case of a resonance circuit

Describe the sum of energies occurring

A

In case of a resonance circuit the sum of the magnetic energy of the inductor coil and the electric energy of the capacitor is constant

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
16
Q

Meaning of this equation

A

If displacement x and time t are measured from the state of equillibrium (a), then the displacement of the oscillating mass at phase angle 􏰌 = 􏰑􏰈t can be described by the following equatio

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
17
Q

What is UNDAMPED FREE OSCILLATION?

A

oscillation without energy loss (e.g., without friction). → As a result, the amplitude of the oscillation is constant.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
18
Q

If the spring–mass oscillatory system mentioned in the previous example is free of friction, then the mass displaced from its resting state to x = A will go through an (1)___ (Fig. 3) with (2)___ amplitude for an (3)___ time.

A
  1. undamped free oscillation
  2. constant
  3. infinite
19
Q

If the spring–mass oscillatory system mentioned in the previous example is free of friction, then the mass displaced from its resting state to x = A will go through an undamped free oscillation (Fig. 3) with constant amplitude for an infinite time.

→ In this ideal case, the oscillation is characterized by ____

A

a single line of amplitude A at the given eigenfrequency f0 in the frequency–amplitude plot (spectrum)

20
Q

UNDAMPED FREE OSCILLATION

In this ideal case, the oscillation is characterized by a ___ line of amplitude A at the given eigenfrequency f0 in the frequency–amplitude plot (spectrum) shown on the right side of the Fig. 3.

A

single

21
Q

UNDAMPED FREE OSCILLATION

In this ideal case, the oscillation is characterized by a single line of amplitude A at the given ___ in the frequency–amplitude plot (spectrum) shown on the right side of the Fig. 3.

A

eigenfrequency

22
Q

UNDAMPED FREE OSCILLATION

In this ideal case, the oscillation is characterized by a single line of amplitude A at the given eigenfrequency f0 in the___ shown on the right side of the Fig. 3.

A

frequency–amplitude plot (spectrum)

23
Q

What is DAMPED FREE OSCILLATION?

A

scillation with energy loss (e.g., friction).

→ As a result, the amplitude of the oscillation decays with time.

24
Q

DAMPED FREE OSCILLATION

In real life, (1)___ is always present, thus the energy of the oscillatory system is gradually (2)___, and the amplitude of the oscillation (3)___.

A
  1. friction
  2. dissipated (i.e., it turns into heat)
  3. decreases
25
Q

DAMPED FREE OSCILLATION

If this energy loss is caused by a drag force that is (1)___ to the velocity of the oscillating body (viscous damper) → the damping of the oscillation can be characterized by a (2)___

A
  1. proportional
  2. damping factor 􏰍.
26
Q

DAMPED FREE OSCILLATION

In this case, the amplitude A of the oscillation ___ as indicated by the dashed enveloping curves (Fig. 4).

A

decreases exponentially

27
Q

DAMPED FREE OSCILLATION

the equation of free oscillation is

→ Give the meaning

A

If damping increases, then the amplitude of the oscillation decays more quickly.

→ Notice that the amplitude drops to the e-th (approx. 37%) of its initial value

28
Q

DAMPED FREE OSCILLATION

In case of (1)___ the energy loss per period is so large that the system returns to equilibrium with no oscillation; in this case the motion is (2)____.

A
  1. critical damping
  2. aperiodic
29
Q

What is CRITICAL DAMPING, APERIODIC OSCILLATION?

A

the energy loss per period is so large that the system reaches equilibrium without passing through the equilibrium point.

30
Q

What is DAMPED DRIVEN OSCILLATION?

A

Besides the restoring force, periodic external driving force acts on the oscillatory system replacing the dissipated energy.

→ After some time, a steady state is reached, in which the frequency of the oscillatory system equals to that of the driving force while its amplitude remains constant.

31
Q

DAMPED DRIVEN OSCILLATION

Consider the case when besides the restoring force an additional harmonic (sinusoidal) force acts on the oscillatory system (Fig. 5).

→ This external force of a given frequency and amplitude will induce, force, or drive the oscillatory system resulting in a ___

A

driven oscillation.

32
Q

DAMPED DRIVEN OSCILLATION

The frequency of driven oscillation does not depend on the ____ of the oscillatory system, but – after a certain transition time – it will be equal to the ___

A
  1. eigenfrequency
  2. driving frequency.
33
Q

DAMPED DRIVEN OSCILLATION

The frequency of driven oscillation does not depend on the eigenfrequency of the oscillatory system, but – after a certain transition time – it will be equal to the driving frequency.

→ Why does this happen?

A

Because the mechanical energy of the driving force steadily replaces the dissipated energy caused by damping, the amplitude of the driven oscillation will be constant after the transition time, when steady-state motion is achieved.

34
Q

DAMPED DRIVEN OSCILLATION

the amplitude of the driven oscillation is highly dependent on ___

A

how close the driving frequency is to the eigenfrequency of the oscillatory system.

35
Q

DAMPED DRIVEN OSCILLATION

As the driving frequency increases, the amplitude of the driven oscillation (1)___ first (2)___ then (3)___.

A
  1. increases
  2. slowly
  3. quickly
36
Q

DAMPED DRIVEN OSCILLATION

Around the eigenfrequency, the amplitude might be many times ___ than the driving amplitude.

A

larger

37
Q

DAMPED DRIVEN OSCILLATION

the energy of the driving force is absorbed in the oscillatory system with the ____

A

highest efficiency at the eigenfrequency.

38
Q

DAMPED DRIVEN OSCILLATION

If the driving frequency approaches the eigenfrequency of the oscillatory system, the amplitude of the driven oscillation – depending on the damping – can be very high

→ this phenomenon is the ___

A

resonance

39
Q

DAMPED DRIVEN OSCILLATION

The amplitude–frequency function is called (1)___, and its maximum point is the (2)_____

A
  1. resonance curve
  2. resonance frequency
40
Q

What is RESONANCE?

A

oscillation driven by a frequency close to the eigenfrequency of the system.

→ Amplitudes may become extremely large.

41
Q

What is resonance curve?

A

the amplitude vs. frequency plot of a driven oscillator.

42
Q

What is resonance frequency?

A

the frequency corresponding to the maximum of the resonance curve. Its value is identical to the eigenfrequency (natural frequency).

43
Q

The greater the 􏰍 damping coefficient, the ___

A

shallower the resonance curve.

44
Q

the height of the peak decreases

→ the resonance frequency shifts somewhat with __

A

increasing damping.

Biophysics LAB 1ST SEM (21 decks)

Brainscape helps you reach your goals faster, through stronger study habits.
© 2024 Bold Learning Solutions. Terms and Conditions