Recent content by Dinheiro

Here's what I tried: Let r(t) be the position vector and T(t) such that: T(t) = r'(t)/||r'(t)|| Now, let w(t) be the speed function and v(t) the velocity vector such that: v(t) = (w(t)*T(t)) Deriving: v'(t) = w'(t)T(t) + w(t)T'(t) = a(t) So acceleration is written by the sum of the two...

This is an exercise from the textbook Apostol Vol 1 (page 525, second edition), and I do not know how to prove it: Suppose a curve C is described by two equivalent functions X and Y, where Y(t) = X[u(t)]. Prove that at each point of C the velocity vectors associated with X and Y are parallel...

Oh, thanks, TSny, I didn't see the reply. I got it

Probably not. Imagine, for an instance, |BC| >> |AB| and m>>M, then the period of oscillation must be smaller to compensate the angular momentum and to keep AB in the vertical. So I guess there must be a relation between the masses, period and BC's length as the problem requests

Yes, despise their mass and consider they are a stiff bar

Yes, this is what you should interpret, actually. Let me edit the post

Homework Statement In a thread with a sphere of mass M on one end, another thread BC is suspended with a sphere of mass m (as the image below). The point A executes small oscillations in the horizontal of period T. Find the length L of BC, knowing that B remains straight underneath A at all...

Actually, I didn't solve it this way, but nice one though! Thanks, hallsoflvy

Great, Ray! I didn't know about this book, though. Thanks

Those were basically my ideas, I just didn't write down my complete attempt at the solution, sorry. But I could find out what was missing in my resolution xD Thanks, Ray

Homework Statement Calculate cos\frac{2\pi}{2n+1} + cos\frac{4\pi}{2n+1} + cos\frac{6\pi}{2n+1} + ... + cos\frac{2n\pi}{2n+1} Homework Equations Complex equations, maybe :p The Attempt at a Solution Let's say z^{2n+1} = 1 The sum is equivalent to the sum of the real even...

Homework Statement Let Ω be the universe and A1, A2, A3, ..., An the subsets of Ω. Prove that the number of elements of Ω that belongs to exactly p (p≤n) of the sets A1, A2, A3, ..., An is \sum_{k=0}^{n-p}(-1)^k\binom{p+k}{k}S_{p+k} in which S_{0} = |\Omega| S_{1} =...

Great! Thanks, haruspex!

c = 1, so that Q(y²+2y+1) = Q[(y+1)²] and, therefore, Q[(y+1)²]=Q²[(y+1)] Great, haruspex! Now, Let y+1 = z Q(z²)=Q²(z) Now, I got stucked, how can I really prove Q(z) = (z+1)^n from it? I can guess the answer, but I couldn't really demonstrate it

Let me retry the problem