All Questions
Tagged with harmonic-oscillator resonance
79
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What are the different types of resonances in forced oscillation systems?
I'm currently studying resonances in systems subjected to forced oscillations and have come across various terms and cases that I'd like to understand more clearly. Specifically, I am analyzing a ...
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1
answer
73
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Calculating the resonance frequency of a spring based on adding additional mass
I have a following problem. I have a spring of unknown spring constant and resonance frequency. I can measure only the force on the spring and the change in length of the spring. I can add mass and ...
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1
answer
51
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How is a resonant bandpass filter similar/different from a damped mass-spring oscillator? They seem to behave both similar and different in testing
Background
I am using resonant bandpass filters as musical oscillators. One can excite an array of them at harmonic frequencies and given Q values for a note by, for example, running a burst of noise ...
- 321
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Modeling a viscoelastic string with a collection of damped spring oscillators? (To replace finite difference model.) How to find $Q$ per harmonic?
Background
I have simulated a vibrating viscoelastic string fixed at each end under tension using finite difference modeling. Most simply this can be done using Kelvin-Voigt style mass-spring dampers ...
- 321
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Force-dependency of frequency response of driven harmonic oscillator with damping
For a driven harmonic oscillator with damping of the form
\begin{equation}
\ddot{x} + 2\xi\omega_0\dot{x} + \omega_0^2x = \frac{F_0}{m}cos(wt)
\end{equation}
with damping ratio $\xi$ and natural ...
- 11
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General solution for Parametric amplification in harmonic oscillator
It is well known that for the simple harmonic oscillator of the form
$$
\frac{d^{2}x}{dt^{2}} = -\omega_{s}^{2}x
$$
where $\omega_{s}$ is the resonant frequency of the oscillation, has the general ...
- 124
1
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1
answer
238
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Spring constant of typical flute style champagne glass?
I am a high school student doing a lab report on the relationship between height and resonance frequency of champagne glasses, using the "singing glasses" method where you rub your finger ...
1
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1
answer
58
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What is the phase of a vibrating beam?
In my lecture notes, when talking about AFM Cantilever, there is graph shown below with following caption:
Resonance of a vibrating beam.
Amplitude (a) and phase (b) of a beam driven at a frequency $...
- 33
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1
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159
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Exciting a normal mode of $N$ coupled oscillator with driving force
Suppose we have $N$ coupled oscillator with the fixed ends.
We can find the normal modes of this system by considering an infinite system and using space translation symmetry to diagonalize the ...
- 436
8
votes
7
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Is resonance a general property of second-order differential equations?
I have read at this site as an answer at a question about how antennas work but that is not important
The resonant frequency of an antenna is determined by its constitution. Mathematically speaking, ...
16
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3
answers
3k
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How does the string of an acoustic guitar transfer energy to the guitar's body?
I've learned through the answer to this post that the purpose of the soundboard of an acoustic guitar is to match the impedance of air, facilitating the energy transfer from the strings to the sound ...
2
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1
answer
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Why damping affect natural frequency of simple harmonic motion? [duplicate]
I am curious about that since damping will not affect frequency of SHM, then why it does affect on the natural frequency of the SHM. In the resonance damping graph the peak amplitude become lower but ...
- 83
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How can I mathematically describe the reflected sound waves in an open tube?
When a sinusoidal sound wave passes through a tube open at both ends, it will get reflected when it reaches the end of the tube. The reflected wave will itself reflect when it reaches the opposite end ...
9
votes
1
answer
816
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Intuition behind the differential equation for forced oscillations
The differential equation for forced oscillation is:
$$m \ddot{x} + b\dot{x}+kx = F_{o}\sin(\omega''t)$$
I don't find this equation intuitively satisfying. My mind tends to think that as $F_{o}\sin(\...
- 215
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At resonance, there is infinite oscillation (new)
As per a previous question:
Transient behavour For a driven harmonic oscillator:
I was trying to show an exponential increase in amplitude using the transient solution, however I still got the sake ...
- 6,636