Differential equation, coupled oscillator, relative movement

[Lindsayyyy]

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:

$$mr''=-kr$$

Homework Equations

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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 don't get there. Any hints?

Thanks in advance

 

[BruceW]

Is this really a homework question? If not, just look up reduced mass on wikipedia. If it is homework, you should write out an attempt, according to physics forum's rules (they are strict on this)