Consider the particle of mass m located in the center of a box of sides 2l and constrained to move in the horizontal plane by the four identical and linearly elastic springs with spring constant k each. Each of the springs has free length l. Let O be the origin of the coordinate system located at the center of the box. To derive the equation of motion of the particle, we displace the mass particle now to a position P with coordinates (x, y). Then, derive (i) the forces in each of the spring as they act on the mass particle, (ii) the general equations for motion of the particle when in position given by (x, y). Note: you are not to make any assumptions regarding the size of displacement relative to the size of the box other than that the springs never get compressed to zero length