Zwiebach 9.3e: Relating τ to X0 & Angular Frequency

[ehrenfest]

Homework Statement

I can relate tau and X0 by:

$$\tau = \frac{X^0}{2 \sqrt{2} \alpha' p^+ }$$

Why does that mean the angular frequency is

$$\frac{1}{2 \sqrt{2} \alpha' p^+ }$$

?

Homework Equations

The Attempt at a Solution

 

[Jimmy Snyder]

$$\tau = \frac{X^0}{2 \sqrt{2} \alpha' p^+ }$$

Take this and plug it into the equations for $X^{(2)}$ and $X^{(3)}$.