1. The problem statement, all variables and given/known data The mass is connected to 4 springs, each connected to a corner of a square with sides √2 a. The springs have spring constants k and natural length a/2. Show the frequency of the mass when it is displaced by d << a towards one of the corners is √(3k/m) 2. Relevant equations F=kx 3. The attempt at a solution When in equilibrium the springs are length a. The forces acting in the same direction of motion would be (a/2 - d)k and -(a/2 + d)k since the spring is already stretch by a/2. I am having trouble finding the vertical forces acting on the mass by the other 2 springs. The length of the spring would be stretched to √(a^2 + d^2) so the force would be (√(a^2 + d^2) - a/2)k but I need to find the vertical component of this force. Working backwards I find that the vertical force on each of the springs must be kd/2 so that (a/2 -d)k - (a/2 +d)k - kd/2 - kd/2 => -3dk so I can move on to use ma = -3xk etc to find the answer. I see a link between being stretched twice its length already and having k/2 but I am not sure why. Many thanks.