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## Homework Statement

(The picture is having trouble being directed so I attached it)

Hey guys, I'm trying to figure out the normal modes of a pendulum with two different masses. The lengths of the strings are the same and the weight of the strings are negligible.

I can easily find everything if the masses are equal but when the masses are different it kind of screws me up.

## Homework Equations

F=ma

F

_{s}=k(x

_{1}-x

_{2})=kΔx

m

_{1}*a

_{1}=-m

_{1}*g*(x

_{1}/l)-kΔx

m

_{2}*a

_{2}=-m

_{2}*g*(x

_{2}/l)-kΔx

## The Attempt at a Solution

x(double dot)

_{n}=a

_{n}

Working it all out I get:

a

_{1}+a

_{2}+(g/l)*(x

_{1}+x

_{2})+Δx((k/m

_{1})-(k/m

_{2}))

This doesn't help me get a simple solution like x(t)=A*cos(ωt+[itex]\phi[/itex]) because of the addition of the Δx((k/m

_{1})-(k/m

_{2}))