Consider an ideal spring that has an unstretched length l_0. Assume the spring has a constant k. Suppose the spring is attached to an cart of mass m that lies on a frictionless plane that is inclined by an angle theta from the horizontal. Let g denote the gravitational constant The given quantities in this problem are l_0, m, k, theta, and g. a) The spring stretches slightly to a new length l>l_0 to hold the cart in equilibrium. Find the length l in terms of the given quantities. b) Now move the cart up along the ramp so that the spring is compressed a distance x from the unstretched length l_0. Then the cart is released from rest What is the velocity of the cart when the spring has first returned to its unstretched length l_0? c) What is the period of oscillation of the cart?