- #1

- 15

- 0

## Homework Statement

Find the perturbation approximation of the following in terms of powers of θ

_{0}.

[tex]T=\sqrt{\frac{8L}{g}}\int^{\theta_0}_{0} \frac{d\theta}{\sqrt{cos\theta - cos\theta_0}}[/tex]

It is helpful to first perform the change of variable u = θ/θ

_{0}in the integral

## Homework Equations

so the relevant equations are the taylor expansion of θ

_{0}, which would be

θ

_{0}=θ

_{00}+εθ

_{01}+ε

^{2}θ

_{02}/2

## The Attempt at a Solution

so then making the change of variable suggested, we have

[tex]T=\sqrt{\frac{8L}{g}}\int^{\theta_0}_{0} \frac{\theta_0 du}{\sqrt{cos(u\theta_0) - cos\theta_0}}[/tex]

is it correct to say that the perturbation approximation is then

[tex]\frac{\theta_0_0 + \epsilon \theta_0_1+

\frac{\epsilon^2 \theta_0_2}{2}...}{\sqrt{cos(u\theta_0_0)-\epsilon sin(u\theta_0_1)-\epsilon^2cos(u\theta_0_2)-cost\theta_0_0)-\epsilon sin(theta_0_1)-\epsilon^2cos(\theta_0_2)...-cos\theta_0}}=0[/tex]

or am i doing something wrong?