# Second order differential equation

1. Mar 24, 2014

### elevenb

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

The solution is there, its to do with part (c), I would realy appreciate it if someone would explain how they make the jumps - especially to the second last equation

2. Mar 24, 2014

### AlephZero

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. Mar 24, 2014

### elevenb

Ignore- spotted mistake

Last edited: Mar 24, 2014