Recent content by Duke Le

Thanks for replying! I edited the post. So the answer for this question is: y(t) = ∑(delta(t - 4k)) From y(t) i can show that a[k] = 1 for all k. But I couldn't find y(t) given that a[k] = 1 since it didn't converge.

We have: Period T = 4, so fundamental frequency w0 = pi/2. This question seems sooo easy. But when I use the integral: x(t) = Σa[k] * exp(i*k*pi/2*t). I get 1 + sum(cos(k*pi/2*t)), which does not converge. Where did I went wrong ? Thanks a lot for your help.

Okay that's where things went wrong. Thanks a lot ! Thread marked solved.

I'll add a picture because I don't have enough vocabulary yet. For the dy ≅ arc length approximation, I meant: dy ≅ a when dy is very small. Is this approximation valid ?

I haven't really learned polar coordinate yet, only its definition and simple calculation. I did try integration using dθ and Rcos(θ) though, it was: I = 4\int_{0}^{\frac{\pi }{2}} \frac{d\theta }{2 \pi}MR^2 and it gave the correct result. I just had no idea why the other formula didn't work...

I think I have found the mistake. My intention for integrating from 0 to R was that dy ~= arc length from y to y+dy (moving vertically in y+ direction), I guess that approximation is wrong here :D The upper limit should be R*pi/2

Homework Statement Prove the formula for inertia of a ring (2D circle) about its central axis. Homework Equations I = MR^2 Where: M: total mass of the ring R: radius of the ring The Attempt at a Solution - So I need to prove the formula above. - First, I divide the ring into 4...