Recent content by PragmaticYak

Took another crack at this problem. I’ll show the part after proving that every element of ##G## can be written as ##x^{-1}\sigma(x)##. Let ##x \in G##. Then ##x = y^{-1}\sigma(y)## for some ##y \in G##. Now ##\sigma(x) = \sigma(y^{-1}\sigma(y)) = \sigma(y^{-1})y##. Rearranging, ##y^{-1} =...

I did not use the hint for this problem. Here is my attempt at a proof: Proof: Note first that ##σ(σ(x)) = x## for all ##x \in G##. Then ##σ^{-1}(σ(σ(x))) = σ(x) = σ^{-1}(x) = σ(x^{-1})##. Now consider ##σ(gh)## for ##g, h \in G##. We have that ##σ(gh) = σ((gh)^{-1}) = σ(h^{-1}g^{-1})##...

Thank you!

The oscillator's initial energy can be found by considering when all of its energy is potential energy. Eo = (1/2)kA2 = (1/2)mω2A2 = (1/2)me(2πν)2A2 = 2meπ2ν2A2 where me is the mass of an electron. With this in mind, the energy dissipated after one cycle is given by ΔE = E(0) - E(1/ν) = Eo -...

Currently a college student studying computer engineering. I completed a physics minor three years ago but have been dipping in physics textbooks ever since. Interests include golf, roller coasters, and electronic music production.