Second order differential equation

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  • #2
AlephZero
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They used the Binomial theorem.
$$\frac{1}{(d + \Delta d)^2} =\frac{1}{d^2}\left(1 + \frac{\Delta d}{d}\right)^{-2}
= \frac{1}{d^2}\left(1 - 2\frac{\Delta d}{d} + \cdots\right)$$

Everything before that looks like straightforward algebra. The last step to find ##\omega## is the standard solution of the differential equation for simple harmonic motion.
 
  • #3
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Ignore- spotted mistake
 
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