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...
Hi,
I'm just wondering if someone could help me better understand how the Fizeau interferometer works...
http://upload.wikimedia.org/wikipedia/commons/2/2f/Fizeau_interferometer_testing_optical_flat.svg
From my understanding, the source shines light through a collimating lens and the light...
my only concern with that type of setup is accuracy. would the capacitance gauge not have different levels of capacitance as it moves about the stage? There are other metal pieces and electronics nearby
Hi, thanks for your reply.
yes. I did try using the fact that cos(-theta) = cos(theta). But this limits the number of rotations I of theta because I have to introduce arccos, right? So I really only get a half rotation. I COULD just shift the graph over to see the negative values of theta, but...
Polar Coordinates --- Graphing the points of when theta<0
Hi everyone,
I'm working with an online graphing program desmos.com. It's great, and actually tons of fun.
I'm currently working with polar coordinates but the only flaw of this grapher is that when working with polar coordinates...
THanks for you replies.
Just to clarify, I intend to level the steel plate with respect to the stage on which the interferometer is set up. The stage should suspend the interferometer above the plate and move it parallel to the surface of the plate.
If I did have a stage that could maintain a...
Laser Interferometer--Need advice/opinions about design.
Hey Everyone,
I'm in the midst of designing a laser interferometry system to measure flatness and to level a stainless steel plate. It's a really simple design and I'm wondering what the drawbacks are for this type of system. I'm just...
WOW THANKS SO MUCH! that's so helpful. You're a life saver, really.
Just for my own understanding... an annoying question, perhaps: How does it calculate that? Angular velocity must appear somewhere in those equations, no? Although I suppose the calculator can figure out RPMs based off of the...
thanks!
first, I just want to apologize for my elementary understanding of all this, I'm still a junior in high school and am just working on this project in one of my shop classes. I'm interested in all the math and physics involved, I just don't have all the tools yet. So thank you so much...
Radial Flow Water Pump--How to calculate Watts required to power it
Hi all,
I'm currently working on an independent project where I'm building a radial flow water pump to be sent to a village in Senegal. I'm having trouble figuring out what motor to use to power this water pump and how much...