x(t) = A cos(wt+b)

A group of us has gathered in my room. This assignment is due tomorrow, and we're fast approaching the point where we start counting down to that due date in hours. But this class is demanding a significant change in how we perceive the world, and so far none of us has been able to make that leap on our own. So here we are, with our notes and books, hoping that together we'll be able to make some sense of this before it comes time to turn in our homework.

"So we just apply this equation, right?" one person asks.

"That's what is says. So we need to know the potential and kinetic energies."

"Well, that should be easy. But I tried that, and the math got ugly and I got scared so I stopped."

"It should be easy. This is the first assignment of the semester. It just can't be that complicated."

As the three of us argue back and forth, a fourth person has been quietly intent on his paper. He finally holds up the drawing he's made. "I think this is the problem. We should be using cylindrical coordinates, not spherical."

"Are you sure? Everything's in spherical."

"Yeah, but look here. See how the forces are directed? I think it's got to be cylindrical."

"Well, it's worth a shot."

We turn our heads back to our papers, sketching and working out the math for a few silent minutes. Then we're quiet for a few minutes more.

"Gosh that's beautiful."

"It can't be that simple, though, right?"

"Weren't you just complaining that it couldn't be that complicated?"

"But it can't be this simple."

"I think that's the point. It is supposed to be this simple and elegant."

"Well, let's hope the rest of them come this easily."

It's a few hours more before we've completed the set to everyone's satisfaction, arguing theory and algebra as we go. But we're ultimately finished sooner than anyone expected to be. There's time to get a good night's sleep, even. We split up, optimistic that this class won't be as hard as we've been led to believe.

It's only the first assignment, though. A week later we're back in the same place, as confused as ever, wondering once again how to convert the presented problem into a simple harmonic oscillator, the only system that makes complete mathematical sense.