Recent content by Gavran

You are correct. Mechanical energy can be potential energy too. Elastic energy is the mechanical potential energy, but it does not affect the categorization that I mentioned in post #3. The same holds for electrical energy. There is energy of charges due to their position in an electric field...

I am unsure of what to say here. There are those who will tell you that Vbf is equivalent to Vb - Vf, and there are those who will tell you that Vbf is equivalent to Vf - Vb. If your choice is Vbf=Vf-Vb, your calculations are correct. The points B and C are at the same potential, so you can...

You ask about the difference between thermal energy and mechanical energy. Both are two different forms of kinetic energy, which is the energy of motion. All types of kinetic energy can be categorized as radiant energy, thermal energy, sound energy, electrical energy, and mechanical energy...

You are wrong. For instance, in the case of a moving particle with a constant velocity, a position change of a moving particle cannot be interpreted as a disturbance of an equilibrium state. My apologies for post #26. The definition “In mathematics and physical science, a wave is a propagating...

Very similar to post #6. $$ a^0=a^{x-x}=\frac{a^x}{a^x}=1 $$

In my opinion, your definition is correct, but it is incomplete. I agree with @kuruman (post #5) that a wave in classical physics does not include a matter transfer.

"While waves are ubiquitous features of physical systems, no single definition adequately describes the topic." (from Wikipedia)

Clearly, the equation ## 4x^5u''+12x^2u'-4u=0 ## is not a Cauchy–Euler equation, and it cannot be solved by the standard method, which is applicable to Cauchy–Euler equations.

Analytical solution by using Vieta's substitution: ## \begin{align} &a^3-9a^2+21a-3=0\nonumber\\ &a^3-3a^23+3a9-27-3a9+27+21a-3=0\nonumber\\ &(a-3)^3-6a+24=0\nonumber\\ &(a-3)^3-6a+18-18+24=0\nonumber\\ &(a-3)^3-6(a-3)+6=0\nonumber\\ &a-3=w+\frac{6}{3w}=w+\frac{2}{w}\implies...

Let ## (x_1,y_1) ## be a point on the curve ## f(x)=4-x^2 ##, which is the closest point on the curve ## f(x) ## to the curve ## g(x)=(x-3)^2 ##, and let ## (x_1+a,y_1+b) ## be a point on the curve ## g(x)=(x-3)^2 ##, which is the closest point on the curve ## g(x) ## to the curve ## f(x) ##...

There are Figures 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, and 19 in the same text (https://cdn.prod.website-files.com/5dc3329c429c1a9866f49d34/5e37131bc62330e7ed1cedb0_3phXfmrs_GATech.pdf pages 12, 13, 14, 15, 16, and 17), which demonstrate how transformer terminals are connected with windings.

It depends on how X1, X2, and X3 are interconnected with W4, W5, and W6. See again Figure 4-D7 (the third image on the right).

Yes, you are right. That means X1 lags H1 by 30° in group 1, and X1 lags H1 by 330° in group 11. Both examples are correct. See Figure 4 - D7 from https://cdn.prod.website-files.com/5dc3329c429c1a9866f49d34/5e37131bc62330e7ed1cedb0_3phXfmrs_GATech.pdf (page 7).

This is group 1. If H1 points at 12 o'clock, X1 will point at 1 o'clock. This is group 11. If H1 points at 12 o'clock, X1 will point at 11 o'clock.

The substitution ## y_1=10^y ## simplifies the equation $$ 10^ydy=\frac{dx}{x\ln10} $$ to the equation ## dy_1=dx/x ##. The general case can be obtained by replacing ## 10 ## in the substitution ## y_1=10^y ## with ## b ##, where ## b\gt0 ## and ## b\neq1 ##, while the equation ## dy_1=dx/x ##...