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Results tagged with linear-systems
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user 1325
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.
8
votes
How to get "complex exponential" form of wave equation out of "sinusoidal form"?
As user1104 commented, you use Euler's identity:
$$ e^{ix} = \cos(x) + i \space \sin(x) $$
so:
$$ \sin(kx-\omega t) = \frac{ e^{i(kx-\omega t)} - e^{-i(kx-\omega t)}}{2i} $$
But we wouldn't normal …
- 363k
12
votes
The ubiquitous Planewave Ansatz
In many cases our systems are described by linear differential equations, and these have the property that any linear combination of solutions to the differential equation is also a solution to the di …
- 363k
10
votes
Accepted
The sum of all external forces acting on all the particles is equal to the total external fo...
Since you seem happy about the internal forces let's ignore them and just set them all to zero so only consider external forces.
The total momentum $P$ is just the sum of all the individual momenta:
…
- 363k