Questions tagged [linear-systems]
A linear system is a mathematical model of a system based on the use of a linear operator. A system is linear if and only if it satisfies the superposition principle, or equivalently both the additivity and homogeneity properties, without restrictions.
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Do all nonlinear systems store energy?
I would like to clarify, this question comes from my own curiosity while solving for nonlinear differential equations. I have noticed that I lack the fundamental understanding of linearity/...
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Why are forces superimposable in Classical Mechanics? Does this also apply in higher theories like General Relativity and Quantum Mechanics?
In classical mechanics, forces are treated as vectors and are added linearly. Is this principle to be treated as an axiom or is there some underlying principle from which this is derived? And given ...
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What are the limitations of Nodal Analysis?
Yea, that's the question basically. What are the limitations of Nodal Analysis?
Like, for example take the following case, we have to find out the net capacitance between A and B.
Now I want to solve ...
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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 ...
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Mirror image Electric field and potential
pg
My book says the electric field due to a positive point charge at a certain distance from the surface of flat, infinite earthed conductor can be obtained by introducing a virtual negative mirror ...
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Solutions for nonrelativistic-matter perturbations
I'm studying the nonrelativistic-matter perturbations if the expansion of the Universe
is driven by a combination of components.
I'm currently Following this document (The growth of density ...
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To calculate the resultant resistance of a circuit can you use all possible paths and assume they're parallel? [duplicate]
To calculate the resultant resistance of a circuit can you use all possible paths and assume they're parallel?
Say I have a circuit like this:
And I want to determine the resistance between x and y.
...
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How to demonstrate in a simple way that this system of differential equations form a damped harmonic oscillator? [closed]
How may I demonstrate in the most simple way that the following system of differential equation form a damped harmonic oscillator ?
$$
\dot x = -\alpha_x x - \omega y \\
\dot y = -\alpha_y y + \omega ...
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How to justify sound propagation is a linear time-invariant (LTI) system?
Background
A linear time-invariant (LTI) system (black box) is one described by the system:
\begin{align}
\dot{\xi}(t) & = A\xi(t) + B\omega(t), \; \xi(0) = 0 \label{eq-abc-1}\\
\lambda(t)...
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How to solve the coupled equation of motion? [closed]
there we have the EOM:
\begin{align*}
\alpha q_{2} + \lambda - \ddot{q}_1=0 \\
\alpha q_{1} + \lambda - \ddot{q}_2=0
\end{align*}
and $q_{i}$ is the canonical coordinates. Can I use the Fourier ...
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Gravitational field at a point $P$ in a small hole dug in a thin spherical shell?
I am supposed to find the field at a point $P$ in a hole, I initially thought that since the field inside is $0$ initally, now it must be $GM/R^2$ but that is not so, since we cannot assume it to ...
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Why is time period same even if you give an impulse perpendicular to the spring?
It all started with this question.
There are three different ways to solve this but one way is using kepler's second law. $\frac{dA}{dt}=\frac{L}{2m}.$ This applies because angular momentum is ...
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Coupled oscillators and stability of equilibrium points
My question is about parts (e) and (f). I have found the matrix to equation of motion to be $\frac{d}{dt}\begin{bmatrix} x_1 \\ x_2 \\ p_1 \\ p_2\end{bmatrix} = \begin{bmatrix} 0 & 0 & 1 & ...
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Do the solutions to Maxwell's equations form a group?
How many solutions are there for Maxwell's equations? (Or rather, is there a finite number of them?)
Regardless of how many solutions to these equations exist, could we claim they form a group? If so,...
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Possibility of complex EM waves
I'm currently studying Quantum Mechanics, and I have just been presented Schrödinger's (time dependent) equation. Of course, the first solution to said equation I've been taught is that of a (complex) ...
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