Hi,
Is there a proof that complex replacement is a valid way to solve a differential equation? I'm lacking some intuition on the idea that under any algebraic manipulations the real and imaginary parts of an expression don't influence each other.
For example, if I'm given:
$$p(D) x = cos(t)$$...
I'm actually just learning about this myself. Let me see if I can take a stab at answering this, and hopefully either 1) we can work it out together or 2) someone will correct me.
Here's my take:
Essentially what you have from the fundamental matrix is a collection of column vectors, each of...
The equations I'm getting when I solve the differential equations seem to imply that the amplitude of oscillation does not vary in time.
For example, if I have
x'' + ω02x = cos(ωt)
If we suppose that ω≠ω0,
then the general solution should look something like:
x(t) = c1cos(ω0t) + c2sin(ω0t)...
The equations I'm getting when I solve the differential equations seem to imply that the amplitude of oscillation does not vary in time.
For example, if I have
x'' + ω02x = cos(ωt)
If we suppose that ω≠ω0,
then the general solution should look something like:
x(t) = c1cos(ω0t) + c2sin(ω0t)...
Hi I'm just having trouble wrapping my head around differential equations with matrices and vectors...
For example:
let y be a vector.
let A(t) be an nxn matrix.
I have the differential equation:
dy/dt = A(t)y
So I think I understand why the solution is
y = ceA(t)
But I'm having trouble...
Hi all,
I'm just beginning calculus and I'm having trouble figuring this one out.
I need to solve this one without using l'hospital's rule.
1. Homework Statement
Find
Limit (sin(4x)/sin(6x)) as x->0
2. Homework Equations
We know that limit (sin(x)/x) as x -> 0 equals...
that would be nice... but the white light VSI approach is necessary for the relatively rougher surface i'll be looking at.
Would you say that this light source:
http://www.thorlabs.com/thorproduct.cfm?partnumber=MCWHL5-C2
with this beam splitter...
Do you think something like this might work?
http://www.thorlabs.com/newgrouppage9.cfm?objectgroup_id=2615
Item MCWHL5-C2
I would probably need an aperture stop
I was under the impression that the steps described in the diagram (before the light even reaches the beam splitter) were steps that were typical of those carried out in a laser before it exits the laser.
how to get a white light beam then?
I'm trying to figure out what these guys did:
http://hh.diva-portal.org/smash/get/diva2:395542/FULLTEXT01.pdf
just from the picture it looks like it might be an optical fibre?
I'm not sure about the wattage but i know that white light interferometry is a common practice.
http://fp.optics.arizona.edu/jcwyant/pdf/Published_Papers/Optical_Testing/WhiteLightInterferometry.pdf
http://www.micromanufacturing.com/content/understanding-scanning-white-light-interferometry...
Hi everyone,
I'm building a white light interferometer and need help choosing and finding a white light source.
I'm using this mirau objective:
http://www.edmundoptics.com/microscopy/infinity-corrected-objectives/nikon-interferometry-objectives/59312
Here is the setup:
I know...