# Differential equation, coupled oscillator, relative movement

Hi everyone

## Homework Statement

Take a look at the drawing. Now I found out the differential equation for this is:

$$\mu \vec{r}''=-k \vec{r}$$ mu is the reduced mass

Now I shall show, with using the generel solution for this differential equation (in cartesian coordinates), that the differential equation looks like the following in polar coordinates:

$$mr''=-kr$$

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## The Attempt at a Solution

I tried it with inserting the solution in the first equation and take a look if I can reform it to the solution which I shall find out, but I just dont get there. Any hints?

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