Recent content by gordon831

Right, forgot Dirichlet conditions. Thanks for the catch!

Hey Physics Forums, Grading an assignment, the current topic is continuous Fourier Transforms. They're trying to prove the convenient property: \mathcal{F} \left[ \frac{d^n}{dx^n} f(x) \right] = (i \omega)^n \mathcal{F} \left[ f(x) \right] So there's a simple way to get it: Let f(x) be...

The work in part (a) and (b) is good! Can you check your calculator result in part (b) though? I calculate a different number: \frac{(15kg)(6.26\frac{m}{s})^2}{(2m)}-(15kg)(9.8\frac{m}{s^2}) = 147N

Yes. Remember, ground is the same everywhere, so, in a sense, you are completing the loop. You began at ground, you ended at ground. I'm not exactly sure what you mean here. Yes, power plants only send electricity to us, we do not send any energy back to power plants to "complete the...

Diagram A is fine. In Diagram B, the voltage on the terminals of the battery are a bit awkward. You see how there is a straight path from the negative terminal of the battery to ground with no other components in the way? This means the voltage there is 0 V, just like in Diagram A (there is a...

Okay, so let me see if I've got this. Let's say I have two vectors, u which has a length of 1 and parallel to the Cartesian x-axis and v which has a length of 1 and is rotated \frac{\pi}{4} rads counter-clockwise from the x-axis. These are position vectors, so the metric doesn't really apply...

Okay, so when I first read your response I was really confused about what it meant for a vector to be "located" at (r,\theta) and I think I'm still a little confused. By specifying (r, \theta), we are defining our basis vectors. If we normalize e_r and e_\theta, we see that \theta is the...

So here's how I developed the metric. One way to develop a covariant metric of a coordinate space is to dot the covariant bases: g_{ij} = \textbf{e}_i \cdot \textbf{e}_j (Source) see (9) To do the dot product, I use my bases defined in Cartesian coordinates so the dot product is simply...

Hey all, I've never taken a formal class on tensor analysis, but I've been trying to learn a few things about it. I was looking at the metric tensor in curvilinear coordinates. This Wikipedia article claims that you can formulate a dot product in curvilinear coordinates through the following...