A particle of mass m is restricted to move without friction on the x-axis. This particle is connected to a fixed point P a distance d from the x axis by a spring with constant k and length at rest l_0. Working in the two-dimensional plane (x, y), we will denote the coordinates of the particle by (x, 0) while the point P has coordinates (0, d). Find the equilibrium positions of the particle and discuss their stability. In the case where the equilibrium positions are stable, find the period of the small oscillations near equilibrium. Hint: You will want to distinguish the cases d > l_0 , and d < l_0 (ignore the special case d = l_0).