Analyzing the Harmonic Oscillator: Maximal Velocity and Turning Points

[voko]

I do not understand how you get 2pi/ As I said, you should have -9/E in the brackets.

 

[CAF123]

I do not understand how you get 2pi/ As I said, you should have -9/E in the brackets.

See my edit before. It's not that I had -9/E which caused me to get 2pi, it was because I said 8 = 2√2!

 

[voko]

The two values are pretty darn close if you ask me. I am not looking forward to rechecking all the algebra again, anyway :)

 

[CAF123]

Not to actually proceed with this method, but would it be possible to go ahead and use the taylor approximations (sin2θ ≈ 2θ and cos2θ ≈ 1- (2θ)^2/2) at the integration stage to show that for small oscillations I recover the same results?

 

[voko]

I guess the most direct way would be to linearize the original integrand. Your method might work, too.

But, in the end of the day, you got an about 1% difference, which I think is very good.