A block \(m\) can slide along a frictionless table top in the \(x, y\) plane, subject to the forces exerted by one spring that lies along the \(x\) axis and has force-constant \(k_{1}\), and another spring that lies along the \(y\) axis and has force-constant \(k_{2}\). Assume the motions of \(m\) are so small that the springs remain essentially perpendicular to one another. Write the Hamiltonian, the Hamilton-Jacobi equation, and solve the equation to find the motions \(x(t)\) and \(y(t)\) of the block.