Questions tagged [damping]
20 questions
7
votes
1 answer
How to calculate critical damping of a system with two springs and a damper (or two springs and two dampers)?
Background
For a simple system where you have a mass attached to a spring and damper in parallel:
We can calculate the critical damping from the equation of motion:
$mx_{tt} + cx_t + kx = 0$
$ms^2 + cs + k = 0$
$s= \frac{-c ±…
mike
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4
votes
5 answers
What's the Q factor of a digital filter's pole?
For the analog S-plane, the Q factor depends on the angle of the complex pole $p$ from the horizontal axis, $\theta = \arg p$:
damping factor $\zeta = \frac{1}{2Q}$, and $\zeta = \cos(\theta)$, and $\theta = \arg(p)$ so $Q = \frac{1}{2…
endolith
- 14,765
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3
votes
2 answers
Is there any solution for this bandpass feedback overload problem (besides increasing sample rate)?
I have been working on a physical modeling string (eg. guitar/piano) synthesizer which is nearing completion. It is based on a modal array of resonant bandpasses, where each bandpass is set by Q and frequency to a given mode/partial of resonance.…
mike
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3
votes
1 answer
General tips for PID tuning of super low-friction actuator?
I realize this question is not directly related to signal processing, however, it's relevant to system analysis which is relevant to most signal processing engineers. There's also no good alternative stack exchange for me to post this question to…
Izzo
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3
votes
1 answer
For a standard second order transfer function, what is the equivalent time domain significance of $\zeta>0.707$?
In frequency domain $\zeta>0.707$ implies no resonant peak in frequency response. But I am unable to correlate what is the exact time domain effect of this? If $\zeta=0.707$ acts like an 'important damping value' in the frequency domain, shouldn't…
Divya K.S
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2
votes
1 answer
How to derive 2nd order Butterworth condition for the damping coefficient mathematically?
The magnitude of 2nd order low pass filter is given as
$$|H(\omega)|^2= \frac{1}{(1-(\frac{\omega}{\omega_o})^2)^2+(\frac{2\zeta\omega}{\omega_o})^2}$$
Now in order to achieve maximally flat within pass band, we take the derivative of this equation…
Yihan Hu
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2
votes
0 answers
Coupling two resonant bandpass filters? (To simulate guitar/piano string effects)
A major part of the sound of a guitar or piano string comes from the coupling of the horizontal and vertical string vibrations. This concept is described in terms of transfer functions here.
This article describes how the interactions between the…
mike
- 419
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2
votes
1 answer
Difference between these frequency response curves
I am thinking about a simple mass-damper system response. Most single DOF systems show a frequency response plot that looks like this:
Note how increasing the damping ratio always reduces the output response, and at high frequencies, the response…
Arlin Sandbulte
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1
vote
0 answers
Quantifying the frequency shift of a delay with LP filtered feedback
I am working at a Karplus-Strong sound synthesis technique where an excitation impulse is subjected to a delay with feedback and a one pole LP filter in the feedback line. The process is simply
y[0]=(x+ky)[-n]
Where x is the input signal, y is the…
elena
- 191
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1
vote
0 answers
Equation for half-damped triangle signal
I have triangle signal, which is damped only at the beginning of ramping phase (blue line in figure).
I want to fit this type of signal. Just now I use symmetric equation, which gives me a damp at the end of ramping also:
$$ y=C +…
zlon
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0
votes
1 answer
Sum of complex exponential signal in MATLAB
I want to create a sum of damped complex exponential signal with the known values of frequency $f$, damping $\alpha$, amplitude $a$ and phase $\phi$ for the $k = 1,2,...,K$ exponentials. Is there already a command in MATLAB that does it? P.S. I…
Neuling
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0
votes
1 answer
Complex damped exponential signal with repetitive poles and the significance of falling factorial
I was modelling a complex damped exponential signal (discrete) with unique poles as below:
\begin{equation}
x = \sum_{k=1}^{K} (a_k e^{(j\phi_k)})(e^{\{(j2\pi f_k - \alpha_k)\Delta t\}t}), \quad t = 0,1,...,N-1
\end{equation}
where $K \in…
Neuling
- 69
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0
votes
1 answer
Pole Magnitude and Damping Ratio relationship
I know that the damping ratio of a system is defined by the angle of the pole, calculated with respect to the left hand side $x$-axis. Could one infer though, that if the magnitude of the poles is small (i.e. the conjugate poles lie closer to the…
giannis gonidelis
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0
votes
1 answer
Modal analysis and frequency response function - interpretation needed
For couple of weeks now, I have been trying to measure cutting forces during machining processes. The system which I am currently examining is highly distorted at high frequencies due to its structural dynamics. My set-up consists of force sensor,…
Daniel
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0
votes
1 answer
What could be the discrepancies between theory and practice when implementing a proportional controller?
I implemented the following proportional controller circuit in practice.
The transfer function of the plant I uses is
$\frac{20}{(s+2)(s+3)}$.
Before doing the experiment, I plotted the root locus plot of the system.
Then after doing the experiment…
suyol854
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