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15 views

Harmonic Oscillator (2DOF) - Do these results seem correct?

I solved a 2DOF system for a buried harmonic oscillator with a forcing function, but I'm not sure what I should be seeing in terms of resonant frequency shift & velocity. The resonant frequency of ...
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3answers
75 views

$Q$-factor for damped oscillator (not driven)?

How would this be defined? Some of the Q-factor definitions I have encountered include: $$Q=2\pi\frac{Energy \space stored}{Mean \space power \space per \space cycle}\\Q=2\pi\frac{Energy \space ...
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2answers
511 views

Why does the length of a pendulum cause different natural frequencies of pendulums in Barton's pendulum?

In Barton's pendulum, the pendulum with string that is the same length, L, as the brass bob (source of driving frequency) has natural frequency equals to the bob's driving frequency. The pendulum ...
2
votes
3answers
233 views

What is a complex phase shift?

In a complex methods course I am taking, we were given an equation for a particular driven harmonic oscillator where the driving force is trigonometric. I have worked out the math and obtained an ...
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3answers
124 views

How LC oscillator is used for generating signals?

I have been trying to understand some practical applications of LC oscialltors and I dont seem to find much information available on net. One consistent application that I see is "LC circuits are used ...
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1answer
283 views

What is the effect of mass on resonance amplitude?

When a system is undergoing forced oscillations, why does reducing the mass of the system cause the frequency response curve to shift downwards? I encountered this problem in a practice paper, but I ...
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1answer
148 views

What is the relationship between excitation and resonance?

From Resonance (particle physics) - Wikipedia: In particle physics, a resonance is the peak located around a certain energy found in differential cross sections of scattering experiments. These ...
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0answers
73 views

What is the mathematical basis behind using a chirp signal to determine the resonant frequency of a second order differential system?

It is a common practise for engineers to try to determine the resonant frequency of a system through a chirp signal. Given a damped oscillating system with displacement $x$, driven by a chirp signal ...
1
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1answer
398 views

Better understanding natural resonance frequency and simple harmonic motion

Let me see if I'm getting this understood correctly. I'm trying to make sure my interpretation of simple harmonic motion is the right interpretation, including my take on resonant frequency. Okay, so ...
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3answers
2k views

Is the displacement of a driving oscillator in phase with the driving force?

In a set up such as the following: I have read in many places that below resonance the driving force is in phase with the harmonic oscillator. I have also read that the driving oscillator is in phase ...
0
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1answer
537 views

Why is the amplitude of a forced vibration lower above resonance than below? [duplicate]

Am I correct in thinking that for a given harmonic oscillator, with constant magnitude driving force, the resultant amplitude of the steady-state motion will be generally lower above resonance than ...
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2answers
280 views

Amplitude of oscillations in non-resonant forced vibrations

I am somewhat confused about the amplitude of forced vibrations at non-resonance driving frequencies. If I was to assume that there was no / negligible damping present, then at resonance, the ...
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2answers
4k views

Natural and Resonance frequencies of a damped oscillator

The damped oscillator equation is \begin{equation} m\ddot{x}+b\dot{x}+kx=0 \end{equation} And its solution has natural frequency $\omega_0$ \begin{equation} \omega_0=\sqrt{\frac{k}{m}-(\frac{b}{2m})...
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1answer
121 views

Meaning of complex oscillation equation

I have the problem of a dampened harmonic oscillation (more concrete a "Pohl wheel" (here is an illustration of it)) whose motion is given by the following differential equation $$J\frac{d^2 \alpha}{d ...
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2answers
527 views

Meaning of “phase delay” in forced oscillations [duplicate]

I'm currently reading about forced oscillations, and in the book (A course in Classical Physics by Alessandro Bettini) I'm using, they start with the equation $$\frac{d^2x}{dt^2} + \gamma\frac{dx}{dt}...
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1answer
863 views

Relationship between volume of water and resonant frequency

I am currently researching the relationship between the volume of water in an object, and the frequency at which resonance occurs. I have conducted an experiment in which I added volumes of water, ...
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2answers
145 views

Simple harmonic resonance

I understand that the driver force will be in phase with the driven velocity at resonance. However, what will happen if I use the same force with the same frequency(resonance frequency) but applied it ...
0
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2answers
379 views

Resonance in an LCR circuit

What's the significance of resonance in an LCR circuit? My book says something like this "Every system has a tendency to oscillate at a particular frequency. This frequency is known as the system'...
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0answers
352 views

What is the resonance frequency of these circuits?

I am learning about RLC circuits, and I understand that the resonant frequency for a circuit where the capacitor and inductor are in series (and there may or may not be a resistor in series as well to ...
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1answer
1k views

Why is the resonance frequency of an undamped oscillator equal to the undamped resonance?

I have read this post: 'How do you define the resonance frequency of a forced damped oscillator?' And I see that the resonant frequency occurs at the undamped oscillation frequency $\omega_0$ as ...
0
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1answer
2k views

Velocity vs Displacement resonance

If we have a driven damped harmonic oscillator: $$ \frac{d^2x}{dt^2}+\gamma\frac{dx}{dt}+\omega^2_0x=\frac{F}{m} e^{i\omega t} $$ amplitude resonant frequency occurs at: $ \omega_R^2 = \omega^2_0x-\...
1
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1answer
385 views

Can you excite coupled pendula at the frequency difference?

Imagine the typical system of coupled oscillators = two pendula joined by a weak spring. The system is oscillating at the complex motion which arises when you displace one pendulum, say pendulum 1, ...
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1answer
280 views

Dependence of Average energy of a Driven Damped Oscillator?

What I don't understand is - How they concluded that the average energy should be zero except near resonance - and how that implies that $\omega$ can be replaced by $\omega_{0}$ in this expression. Am ...
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2answers
1k views

Frequency of Damped Vibrations [duplicate]

In the chapter sound, my book states that the Frequency of damped vibrations is less than the natural frequency but I could not understand this because in damped vibrations the amplitude decreases and ...
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3answers
1k views

Resonant Frequency of 2 mass spring system

So the question goes if I has a spring with spring constant $k$ and two masses attached to this spring (one on either side) what is the resonant frequency of the system in terms of $m$ and $k$? ...
1
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1answer
232 views

Amplitude of damped driven harmonic oscillator [closed]

I have a question that I can reason physically but mathematically I am not sure if my approach is correct. The amplitude of the oscillator is: $$A(\omega) = \frac{QF_{0}}{m}(\frac{1}{\omega_{0} \...
1
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1answer
1k views

Complex resonant frequency not resonant without imaginary part. So can I still just take real part as solution?

I am working with a matrix on a harmonic oscillator problem and the lowest (absolute) frequency $\omega_0$ where the matrix becomes singular is the resonant frequency. Now I obtained this frequency ...
10
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5answers
1k views

A conceptual doubt regarding Forced Oscillations and Resonance

While studying about the Resonance and Forced Oscillations, I came across a graph in my textbook that is given below:- Now, the author writes As the amount of damping increases, the peak shifts ...
2
votes
1answer
212 views

AFM cantilevers driven below resonance?

Is there a physical reason why AFM cantilevers are driven below their resonance frequencies? In all of the AFMs I have used, once you measure the resonance frequency of the cantilever, it is set up ...
0
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1answer
49 views

Resonance of a system featuring a collection of individual resonators?

Suppose you had a number of harmonic oscillators, each with different resonant frequencies in a system. Does this imply that their is an overall system resonance that is dependent on the individual ...
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2answers
187 views

Confusion about the resonance

I get confused with the concept of resonance. Many materials suggest that in order to achieve resonance, the system must undergo simple harmonic force ($F=F_0\sin(\omega t)$), and at the natural ...
1
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1answer
501 views

Undamped Resonance of a Classical Harmonic Oscillator

Consider an undamped harmonic oscillator. It may be driven at it's natural frequency, $\omega_0^2 = \frac{k}{m}$. According to Feynman, and other sources, were this to happen, the amplitude of the ...
5
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3answers
2k views

Physical reason behind having greater amplitude when driving frequency$ < $ natural frequency than that when driving frequency $>$ natural frequency

This is quoted from A.P.French's Vibrations & Waves: If the driving force is of low frequency relative to the natural frequency, we would expect the particle to move essentially with the ...
1
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1answer
658 views

Amplitude-Frequency curve

Given a resonance curve just like this: Could someone explain to me what the physical meaning of the intersection with the ordinate is? At first glance I would say it has to be $(0 | 0) $ since if ...
16
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3answers
8k views

Definition of the $Q$ factor?

According to Wikipedia, the $Q$ factor is defined as: $$Q=2\pi\frac{\mathrm{energy \, \, stored}}{\mathrm{energy \, \,dissipated \, \, per \, \, cycle}}.$$ Here are my questions: Does the energy ...
0
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1answer
615 views

Questions related to resonance/standing-waves and sound

I understand resonance for a simple harmonic oscillator but not for more complex systems like standing waves. How can I be in resonance with the normal mode in an organ pipe? I understand that the ...
0
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2answers
4k views

Resonance and a tuning fork

I carried out this experiment in class: I struck a tuning fork with a hammer. The sound lasted for some time. However, when I connected the tuning fork onto a wooden sounding box, the sound lasted ...
4
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1answer
140 views

Is this oscillator driven?

A mass $m$ is attached to a vertical massless spring or a spring constant $k$. Originally, the spring was relaxed because the mass was held by a clip. Suddenly the clip was released. THe mass dropped ...
4
votes
2answers
2k views

Harmonic Oscillator driven by a Dirac delta-like force

Consider that there is no damping for simplicity. As we know, a driving force of the form $\sin(\omega t)$ will make the oscillator at steady state vibrates at the external frequency $\omega$. What ...
6
votes
1answer
728 views

Can soldiers marching at the right frequency realistically cause a bridge to break?

In my physics class it was suggested that ancient armies had a rough understanding of the idea of a resonant frequency and so they "broke step" when crossing bridges so as to avoid a very high $Q$. I ...
2
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0answers
70 views

Is there an equation that tells you more about the amplitude of an object which is in resonance?

I'm a high school senior and I have to write a paper about resonance and differential equations. I've been searching the Internet for a long time, but I haven't found an equation that is properly ...
3
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2answers
165 views

Does spatial coupling prohibit resonances due to an external source field?

The harmonic oscillator coupled to a sinodial external source $$\frac{\partial^2 x(t)}{\partial t^2}+\omega_0^2 x(t)=F_0\sin(\omega_\text{ext}\ t),$$ has the solution $$x(t)=x(0)\cos(\omega_0 t)+C \...
0
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2answers
2k views

FWHM in resonance amplitude square derivation

Consider a linear harmonic oscillator subject to a periodic force: $$ \ddot x + 2 \beta \dot x + \omega _0 ^2x = f_0\cos \omega t$$ The solution tends to: $$A \cos (\omega t - \delta)$$ where: $$...
18
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1answer
3k views

Why don't tuning forks have three prongs?

I was reading Why tuning forks have two prongs?. The top answer said the reason was to reduce oscillation through the hand holding the other prong. So if having 2 prongs will reduce oscillation loss, ...