All Questions
Tagged with linear-systems classical-mechanics
14 questions
1
vote
3
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178
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Why we take only the real part of a solution as the actual motion?
I am taking Analytical Mechanics, and in Goldstein's book, chapter 6 (page 241) about linear oscillations, he says the following:
"... $\eta_i=Ca_ie^{-i\omega t}$ (6.11) ... It is understood of ...
- 13
1
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1
answer
135
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Kinetic and Potential Energy of a multi degree of freedom (MDOF) system
Consider the following MDOF system:
$M\ddot x+Kx=F$
where $M$ and $K$ are the mass and stiffness matrix respectively, and $x$ and $F$ are the displacement and force vectors.
How can one determine the ...
- 15
0
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1
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678
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Do all objects in a system need to have the same acceleration? [closed]
What is the definition of a system? Could multiple objects accelerating at different magnitudes and directions still be considered a system?
- 59
1
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1
answer
233
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Are non-linear representations important?
In quantum theory, physical states are elements of a Hilbert space, and the transformations must be unitary, implying that the states must transform under a representation of the symmetry group.
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- 442
2
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2
answers
589
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Do Galilean (Euclidean) space transformations implies that time is absolute?
I recently read a paper where it says "if space is universally Euclidean, then time is universal" and I don't understand some key points about the implication.
To put in context, the author ...
- 625
0
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2
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90
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Linear system in polar coordinates [closed]
Unlike the Cartesian coordinates, I find navigating through polar coordinates difficult. Is the system defined by the following Lagrangian $L$ defined in polar coordinates linear?
$$L = \frac{1}{2} m \...
- 113
2
votes
0
answers
184
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Landau & Lifshitz 'Mechanics': How is the potential energy related to additive property of Lagrangian?
By additive property of Lagrangian, I mean following:
Let a system consist of two parts A and B which are not interacting with each other, so A and B will have separate Lagrangians $$L_a,L_b$$ and in ...
- 649
0
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3
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826
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On force being directly proportional to the rate of change of momentum [duplicate]
Newton's second law says that $F_{Net}=\frac{dp}{dt}$.
I do realise that when the net force on a body is zero it keeps its current velocity, so one can infer that the force is somehow related to ...
- 568
1
vote
2
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633
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Congruence transformations of matrices
From the book Analytical Mechanics by Fowles and Cassiday I am studying classical coupled harmonic oscillators. These are systems that are governed by a system of linear second order differential ...
- 11
1
vote
1
answer
178
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Why are all solutions to this system of pendulum differential equations a linear combination of the two given solutions?
I am currently trying to do a lab report for a coupled pendulums experiment in which we find the following linear system of second order differential equations (describing the position as a function ...
- 175
3
votes
1
answer
837
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Applying Kramers-Kronig relation to a simple damped oscillator
I just discovered the Kramers-Kronig relation and am trying to apply it to a simple damped oscillator of the form subjected to an impulse at $t=0$, which is a causal system:
$$m\ddot x + c\dot x + k ...
- 744
7
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2
answers
2k
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When does the principle of superposition apply?
I assumed from my general physics courses that the principle of superposition was just an empirical fact about forces. Then I could understand that derived quantities like the $E$ and $B$ fields ...
- 1,051
3
votes
3
answers
608
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Why is response of system same frequency as driving force frequency
Super basic question: why does a system (to be definite, perhaps assume a collection of coupled harmonic oscillators) respond (in the steady-state, after transient effects have dissipated) with all ...
- 992
0
votes
1
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375
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Microphones, Loudspeaker and their analogies to spring mass system
I have just started studying Microphones and Loudspeakers. I need a good text to refer which can explain their mechanical analogies with simplicity and basics too.
- 55