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Results tagged with linear-systems
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user 26076
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.
1
vote
Accepted
Transfer function analisis
You seem as though you're under the misconception that $s$ is always an imaginary variable. This is not so; from a sophisticated viewpoint, most of the theoretical results about Laplace transforms com …
- 89.3k
1
vote
Can the Kramers–Kronig relation be used to correct transfer function measurements?
I can think of a method that follows from a numerical Hilbert transformer I came up with for estimating the phase of Raman gains, a problem which is very like many handled in spectroscopy. I've never …
- 89.3k
5
votes
Accepted
Is squared motor gearbox ratio proportional to inertia ratio?
Gearboxes belong to a class of linear system that conserves a product of observable quantities by dint of the principle of conservation of energy. For a gearbox, the product $\tau \omega$, where $\tau …
- 89.3k
1
vote
Accepted
Delta to Star/Y Conversions and vice versa in Electric Ciruits
The concept is a special case of a more general topological notion of graph theoretic duality: see the Wikipedia page for Dual Graph.
Graph theoretic duality is "compatible" with the Kirchoff voltag …
- 89.3k
10
votes
Accepted
"Complex Variables Method" in Diff. Eq. - Justification and physical meaning?
When one uses complex variables in this way one never multiplies two variables because the whole system is linear: if $z$ is the oscillating variable and you choose to represent it by a complex number …
- 89.3k
6
votes
Accepted
Why do phasors add like vectors?
Simply because if:
$$R\,\cos(-\omega\,t+\theta) = A \cos(\omega\,t) + B\,\sin(\omega\,t)\tag{1}$$
then:
$$R\,\cos\theta = A\tag{2}$$
$$R\, \sin\theta = B\tag{3}$$
So that the entity $R\angle\theta …
- 89.3k