Problem 3: [Id mints totet'] Spring attached to a mass on a tilted rod Consider a mass m on a spring with spring con- stant k. as illustrated in the figure to the left. where the mass can slide along the rod [with- out friction} which is tilted with respect to the horizontal by an angle it This spring exerts a typical linear spring force so that its poten- tial energy is proportional to the square of the springs length {and the rest length of the spring is eero]. The spring is initially stretched to a length it [as shown in the left image}_~ which is the vertical distance from where the spring is attached to the ceiling to the base of the rod. Gravity points down in this scenario1 such that g = g. The goal of this problem is to understand the equilibrium position yeq illustrated in the right intage. a} [.5 points} Derive an expression [or the potential energy of the mass as a function of the height 1; of the mass above the ground at its position along the slanted rod. [Hint-z: You should find that it can he written as a quadratic function of 1;. Use trig identities to simplify your result] h} (it? points] Find the location of the equilibrium point. yap Determine under what conditions the equilibrium point exists and if it is a stable equilibrium point or not. c} [5 points} 1What is the kinetic energy of the mass at pm if it is released at rest from y = [l {the lowest point on the rod, as illustrated in the left image above]? Note: To help with grading. rst express your answer in terms of the rariahle peg before suhstituting in your result [or yeq from part b}