Recent content by eptheta

It's actually part what periodic functions are. for a periodic function g(x): g(x+P)=g(x) where P is the period. So your function f(x)=sin(x) is as good as f(x)=sin (x \pm n\pi) n=0,1,2... so x=sin^{-1}(y) \pm n\pi now go ahead and put y=0 to get all your x intercepts.

Hi, I am trying to prove that a limit exists at a point using the epsilon delta definition in the complex plane, but I can't seem to reach a conclusion. Here's what I have been trying to get at: \lim_{z\to z_o} z^2+c = {z_o}^2 +c |z^2+c-{z_o}^2-c|<\epsilon \ whenever\ 0<|z-z_o|<\delta...

I didn't integrate anything and got the same answer as you. I used L=L_s cos(\beta) \hat{j} + L_s sin(\beta) (-\hat{r}) \tau=RT sin(\frac{\pi}{2} - \alpha + \beta) \hat{\theta} (got T from F=ma in x and y) then used \frac{dL}{dt}=\tau and got \beta=\frac{2g}{R\omega^2} Can anyone else...

Ah, that's right. I kept thinking that C was acting downwards even though I mentioned that it was in \hat{r} in my previous post. Indeed, it works out fine. Thanks a lot.

Doc, How is point P accelerating any different than the CM is ? From what i can see, the CM is moving with the same acceleration as point P at all times during this motion. And if there is no need to get into an accelerating reference frame when analyzing the CM motion, why is there a need to...

The problem statement A race-car is driving on a circular track, and above a particular speed, the race-car may flip over towards the outside track (inward wheels lift). Frictional force is present. The distance of the center of mass from the ground is L, the distance between the wheels is 2d...

Understood, thanks.

Anyone ?

I have a function in x and y, and I was trying to figure out if it was continuous or not. f(x,y)=\frac{x^2-y^2}{(x^2+y^2)^2} As far as I know, the only problematic point in the domain is (x,y)=(0,0) so I tried to use the \epsilon,\delta definition. My proposed limit at (0,0) being 0...

Actually, the rod I'm talking about is also vertical. Here's an image: The rod is pivoted at O and torque calculations were done about this point. As far as I can see, the weight still contributes a cosθ component to torque. The equation simplifies to \ddot{\theta} + \frac{15k}{4m}\theta...

I know this is 2 years old, but I did the same sum just now and got almost exactly what the OP has, except for one thing: \tau_g=\vec{r} \times \vec {mg} =\frac{L}{2}\hat{r} \times mg (-\hat{j}) =\frac{mgL}{2}([cos\theta\hat{i} +sin\theta\hat{j}] \times -\hat{j})...

While I am back in this thread, I may as well re-ask my original question: Is there a physical limitation to the size of a crystal grown by suspension in a supersaturated solution ? I mean theoretically the crystal should grow indefinitely as long as the concentration is maintained throughout...

I don't even think sucrose is soluble in alcohol. This reminds me of those salt crystal gardens. Several people suggest using ammonia mixed in water as a solvent... Maybe a mixture of alcohol and water (and if so, then ammonia and water) could help keep the solution supersaturated if it does...

Wow, that's big ! Tell me, did you initially plan to grow it uniformly (i.e in its standard crystal configuration) but it went haywire? Or was it your intention to grow a crystal cluster ? I've tried to grow sucrose crystals too but after a certain point(size/volume) they stopped growing and...

Oh my god! Its quartz ! The giant crystal project is all about minerals mined from caves etc. I was wondering about laboratory(or in my case kitchen) grown crystals...