- #1

Ben2

- 37

- 9

- Homework Statement
- "An electron is constrained to move along the axis of the ring of charge in Example 5. Show that the electron can perform oscillations whose frequency is given by ##\omega = \sqrt{frac{eq}{4\pi(\epsilon_0)ma^3}}##. This formula holds only for small oscillations, that is, for x<<a in Fig. 27-10. (Hint: Show that the motion is simple harmonic and use Eq. 15-11." [Halliday & Resnick, Ch. 27, Problem 19]

- Relevant Equations
- ##K=frac{1}{2}(kA^2)\sin^2((\omega)t+\delta)## (15-11)

Showing the motion is simple harmonic seems routine. The 5th equation on p. 674 gives ##E=frac{1}{4\pi\epsilon_0}frac{qx}{(a^2)+(x^2)}^frac{3}{2}##, but matching expressions for ##\omega=k/m## yields only ##x=frac{ea^2}{2}##. Something in the model is escaping me. Thanks for any help offered!