Understanding Resonance Frequency Decrease in Oscillation Systems

In summary: Resonance is displaced to the left on the graph when damping increases because the amplitude of the system at the resonance frequency decrease and the resonance frequency also decreased.
  • #1
Wen
44
0
In an Oscillating system,as damping increases, the amplitude of the system at the resonance frequency decrease and the resonance frequency also decreased. However why does the reasonce freq decrease? I know how to solve for the new amplitude and ang. freq. mathematically but i do not know how to explain the decrease in resonant freq. qualitatively?
Can someone just explain it to me?
 

Attachments

  • damp_6.gif
    damp_6.gif
    2.8 KB · Views: 5,421
Last edited:
Physics news on Phys.org
  • #2
Take a look at the general expression for the damped resonant frequency [itex]\omega_d[/itex].

[tex]\omega_d=\sqrt{\frac{k}{m}-\frac{b^2}{4m^2}}[/tex]

Note that [itex]\frac{k}{m}[/itex] is the undamped resonant frequency [itex]\omega_0[/itex]. If [itex]\omega_0[/itex] is taken to be a constant then [itex]\omega_d[/itex] is seen to be a decreasing function of the damping coefficient [itex]b[/itex].
 
  • #3
damping is friction; a damped oscillator moves slower than an undamped one.
If the oscillator travels slower, it takes longer time to complete an oscillation.
 
  • #4
I'm sorry but Is it so simple? So the phase difference doesn't matter? Why is it known as a mechanical RESPONSE?
 
  • #5
Wen said:
I'm sorry but Is it so simple? So the phase difference doesn't matter? Why is it known as a mechanical RESPONSE?
Simple harmonic motion was known from observations of mechanical systems, e.g. springs, long before electricity was discovered.
 
  • #6
lightgrav said:
damping is friction; a damped oscillator moves slower than an undamped one.
If the oscillator travels slower, it takes longer time to complete an oscillation.

He's not asking why the system moves slower, he's asking why the resonance was displaced.

Wen: I'm sorry but Is it so simple? So the phase difference doesn't matter? Why is it known as a mechanical RESPONSE?

Astronuc: Simple harmonic motion was known from observations of mechanical systems, e.g. springs, long before electricity was discovered.

He's not talking about electricity. Phase differences can crop up in any system that is described with periodic functions, as this one is.
 
  • #7
Wen said:
So the phase difference doesn't matter?

Which phase difference? You didn't specify a forcing function, so all we have here is the natural response.

Why is it known as a mechanical RESPONSE?

Why is what known as a mechanical response? The reason I ask is that the mechanical response for an oscillator is typically a time-varying function of position. But you never referred to such a thing, so I don't know what you mean by "it" in that question.
 
  • #8
Sorry i wasn't specific, what i was asking was that an oscillating system, undergoing forced oscillation by an external periodic force and damping increased. So why did the resonant freq of the enternal force decreases( as seen a shift to the left in the graph)?
Someone mentioned that resonance was displaced? So my qn was why is it displaced to the left on the graph, when damping increases.
 
  • #9
Wen said:
Sorry i wasn't specific, what i was asking was that an oscillating system, undergoing forced oscillation by an external periodic force and damping increased.

That's OK, because it doesn't matter if your oscillator is forced or not. The resonant frequency will be the same either way. Remember that the resonant frequency is found by solving for the natural (that is, unforced) response.

So why did the resonant freq of the enternal force decreases( as seen a shift to the left in the graph)?
Someone mentioned that resonance was displaced? So my qn was why is it displaced to the left on the graph, when damping increases.

I answered that in my first reply.
 

1. What is resonance frequency decrease in oscillation systems?

Resonance frequency decrease in oscillation systems refers to the phenomenon where the natural frequency of an oscillating system decreases due to the presence of a damping force. This can occur in mechanical, electrical, and other types of oscillation systems.

2. What causes resonance frequency decrease?

Resonance frequency decrease is caused by the presence of a damping force, such as friction or resistance, in the oscillation system. This force dissipates energy from the system, causing the amplitude of oscillation to decrease and the resonance frequency to shift.

3. How does resonance frequency decrease affect the behavior of oscillation systems?

Resonance frequency decrease can significantly impact the behavior of oscillation systems. It can decrease the amplitude of oscillation, reduce the system's energy, and change the system's response to external forces. In extreme cases, it can even lead to the system's failure.

4. Can resonance frequency decrease be beneficial in certain applications?

Yes, resonance frequency decrease can be beneficial in some applications. For example, in musical instruments, it can help dampen unwanted overtones and produce a clearer and more pleasing sound. In electrical circuits, it can prevent the system from oscillating uncontrollably and potentially causing damage.

5. How is resonance frequency decrease measured and analyzed?

Resonance frequency decrease can be measured by observing changes in the amplitude and frequency of oscillation in the system. It can also be analyzed using mathematical equations and simulations to understand the effects of damping on the system's behavior. Additionally, experimental techniques such as frequency response analysis can be used to study the system's response to different levels of damping.

Similar threads

  • Introductory Physics Homework Help
Replies
17
Views
277
  • Introductory Physics Homework Help
2
Replies
39
Views
3K
  • Introductory Physics Homework Help
Replies
10
Views
478
  • Introductory Physics Homework Help
Replies
3
Views
2K
  • Introductory Physics Homework Help
Replies
3
Views
951
  • Introductory Physics Homework Help
Replies
1
Views
2K
  • Introductory Physics Homework Help
Replies
7
Views
5K
  • Introductory Physics Homework Help
Replies
6
Views
1K
Replies
4
Views
1K
  • Introductory Physics Homework Help
Replies
3
Views
1K
Back
Top