So the normal mode that is positive would be the symmetric motion of the masses and the negative would be the anitsymmetric? I know I might be way wrong I’m completely new to this.
+Alex Drozd, The signs in the matrix at the top should have been negative, as they were just before that. I had realized my mistake and changed things, but missed that matrix. The math that follows is correct, as far as I can tell.
When you write e^(i * theta), the i represents the imaginary number i = square root of negative 1. (It is "imaginary" as opposed to a "real" number on the number line. It isn't made up or anything like that.) e^(i*theta) = cos (theta) + i sin (theta). If we just ignore the imaginary part, we have the cosine part left. For physical oscillators, that's reasonable to do. For some higher level math and physics, the imaginary part might contain useful information.
+Raimundo Gonzalez, the difference is (mostly) in how they are used. Sine and cosine functions would be used as eigenfunctions to build a function. Eigenvectors build vectors. In the simplest sense, x, y, and z unit vectors are eigenvectors.
i am very delighten by your explanation.good explanation.thank you
Excellent video, sir. It's a shame that seemingly few people came across it, but more so for them than for you. Very insightful, I appreciate it.
Thank you for taking the time to make these brilliant videos they helped me alot. Thank you so very much.
You are very welcome.
will u please make a video for n+1 mass and n spring system
brilliant explanation thank you
+mysciencyvids Thanks for watching. Please share the videos with your friends.
So the normal mode that is positive would be the symmetric motion of the masses and the negative would be the anitsymmetric? I know I might be way wrong I’m completely new to this.
In this case, your deductions are true. You would need to look at each case separately. That being said, the lower modes are typically the simplest.
Physics This Week Sweet, thanks for the helpful videos!
Why do the signs on k change at 6:55?
+Alex Drozd, The signs in the matrix at the top should have been negative, as they were just before that. I had realized my mistake and changed things, but missed that matrix. The math that follows is correct, as far as I can tell.
Hai, i still 10th grade and i wanna ask u why Acos (theta) equal to Ae to the power theta
When you write e^(i * theta), the i represents the imaginary number i = square root of negative 1. (It is "imaginary" as opposed to a "real" number on the number line. It isn't made up or anything like that.) e^(i*theta) = cos (theta) + i sin (theta). If we just ignore the imaginary part, we have the cosine part left. For physical oscillators, that's reasonable to do. For some higher level math and physics, the imaginary part might contain useful information.
Hi! Very helpful set of videos. Question: what would be the difference between an eigenfunction and an eigenvector?
+Raimundo Gonzalez, the difference is (mostly) in how they are used. Sine and cosine functions would be used as eigenfunctions to build a function. Eigenvectors build vectors. In the simplest sense, x, y, and z unit vectors are eigenvectors.