# Recent content by R136a1

1. ### Learning Physics from listening to ipod?

Listening to the Feynman lectures or something similar is a very good idea. But please let this only be a secondary resource and not your main resource for learning. If you don't only rely on this, but are focused on the math and problem solving, then this could be a very good thing.
2. ### Spring with 2 masses free fall

Thank you very much haruspex! I was doing the entire problem with the mindset of someone analyzing an inverse-square gravitational field such as that exterior to a sphere of uniform density, although I have absolutely no idea why I was stuck in this mindset :redface: you'll have to excuse the...
3. ### Spring with 2 masses free fall

Oh sorry I meant to say the opposite of what I actually said. I was thinking of the field external to the sphere of uniform density. Inside it varies linearly with the distance from the center of the sphere of uniform density.
4. ### Spring with 2 masses free fall

Thank you so much mfb. If we let ##u = r_a - r_b - l## in the equation ##m(\ddot{r}_a - \ddot{r}_b) = -2k(r_a - r_b - l) + f(r_a - r_b)## then we get ##m\ddot{u}+ (2k - f)u = fl##. Wouldn't this imply that the new period is ##T = 2\pi \sqrt{\frac{m}{2k - f}}## as opposed to ##T = 2\pi...
5. ### Looking for text on stochastic processes

What about Feller's excellent two volume set on probability? https://www.amazon.com/dp/0471257087/?tag=pfamazon01-20&tag=pfamazon01-20 Especially the second volume seems to have some good stuff. There might also be an introduction to measure theory in the book.
6. ### Spring with 2 masses free fall

I'm not sure I follow, at least with regards to the physical system in this problem. We have a spring with two identical masses one on each end and if the system is allowed to oscillate freely then the period should be ##T = 2\pi \sqrt{\frac{m}{2k}}##. See for example ehild's post here...
7. ### Spring with 2 masses free fall

Thanks for the reply! As for the tidal forces having the same sign: if we imagine the center of mass as a hypothetical particle relative to whom both the top and bottom mass experience tidal forces then shouldn't both the top and bottom mass be accelerating away from the center of mass under...
8. ### Spring with 2 masses free fall

Homework Statement The Attempt at a Solution The reference to exercise 1.7 is not essential. The only part exercise 1.7 that is relevant to this exercise is the following: if a long narrow tube is drilled between antipodal points on a sphere of uniform mass density and two identical...
9. ### Convulation and integration

But ##\int f(x) dx## and ##\int g(x)dx## are just real numbers, no? What is the convolution of two numbers?
10. ### Compactness and Connectedness

See http://planetmath.org/proofofheineboreltheorem under the heading "The case n=1, the closed interval is compact". This contains an elementary proof of the fact that closed intervals in ##\mathbb{R}## are compact. If you already know the Heine-Borel theorem however, then you know that...
11. ### Disjoint Cycles

If you have one cycle, then you can find the inverse by reversing the cycle. So if \sigma = (1 ~2~5~3), then \sigma^{-1} = (3~5~2~1) Then if you have a more general form, then you can calculate the inverse by the formula ##(\sigma\tau)^{-1}= \tau^{-1}\sigma^{-1}##. For example, if you have...
12. ### Compactness and Connectedness

What is your definition of compact? Right!
13. ### Compactness and Connectedness

Yes to both. Try to find counterexamples.
14. ### Disjoint Cycles

How did you define ##\pi^\sigma##? Did you define it as ##\sigma \circ \pi \circ \sigma^{-1}##?
15. ### Two exercises on complex sequences (one about Mandelbrot set)

You have |z_0| = 0 |z_1| = |c| |z_2| = |z_1^2 + c| \ |c| |c+1|\geq |c| |z_3| = |(c^2 + c)^2 + c| = |c^2 (c +1)^2 + c| = |c| |c(c+1)^2 + 1|\geq |c|( |c|^2 |c+1|^2 - 1) \geq |c| (|c|^2 -1) \geq |c|^2 where I make fundamental use of the inequality ##|a-b| \geq ||a| - |b||##.