SHM in a horizontal plane: 4 springs

[mmh37]

a point mass is constrained to move in a horizontal plane and is attached to four fixed pegs by 4 light springs. The four pegs are arranged at the corners of a square of side root2*a. Each spring has a natural length of a/2 and a spring constant a. If the mass is displaced towards one corner through a small distance d<<a and is then released from rest, what is the angular frequencyof this SHM?

So far I have tried to resolve forced in x and y direction but that didn't work. This seems to be quite tough. Thanks for any hints.

 

[big man]

Do you have a diagram of the system at all?

 

[mmh37]

well, from the question, I think this is how it looks like (note that the system is arranged in the horizontal plane):

Can anyone please try to help - this is really important (exams start in one week!). Thanks so much!

 

[Doc Al]

Each spring has a natural length of a/2 and a spring constant a.

I assume that's a typo and you meant a spring constant "k" (or something), not "a" (which is a length).

I also assume that if you only had one spring, with spring constant k, you would know how to find the angular frequency.

For this problem, what you have to do is find the effective spring constant. Hint: As the mass is displaced towards one corner, what is the restoring force on it?

 

[Hootenanny]

I assume that's a typo and you meant a spring constant "k" (or something), not "a" (which is a length).[

That threw me also Doc, I didn't think that it could be a typo

~H