How Do You Calculate Omega for a Mass Between Two Different Springs?

[Keesjan]

Homework Statement

Hey

The part of the question that i am not all the sure about is Newtons second law.
and the Omega
the Situation is as followed

]/\/\/k1\/\/\[m]/\/\/k2/\/\[

There are 2 springs k1,k2 and a mass in between.

Homework Equations

F=ma and F=-kx

x=Asin(omega(t)+theta)

The Attempt at a Solution

Now i find it a little confusing because there are 2 springs with both different constants.

I think the solution is

ma=(-k1+k2)x which turns into ma=(k2-k1)x so a+((k2-k1)x)/m=0
now when finding the solution for Omega i get

omega= -sqr(((k2-k1)x)/m) now the (-) sign is annoying me, usually its not there,
so i think i might made a mistake with the (k2-k1),

thanks for the help

Homework Statement

Homework Equations

The Attempt at a Solution

 

[dacruick]

There is a property for the system you are trying to figure out that I can't quite recall, but subtracting the constants is not right. Think about the physics of the situation.

]/\/\/\/\/\/\/\/\/k1\/\/\[m]/\/\/k2/\/\/\/\/\/\/\/\/[ this then goes to this
]\/\/k1\/\/\[m]\/\/\/\/\/\/\/\/k2\/\/\/\/\/\/\/\/\/\/[
so you know that this point k1 is compressed to it is pushing m to the right.
you also know that k2 is stretched, so it will pull m also to the right. So you know that these two forces must add, my guess would be that it is by a factor of 1/root(2). You can find this easily online, let me know what the answer ends up being