Problem 1 Consider the frictionless rod; i.e. ,8 = I]. The equation ofmotion becomes d3?" 2 _ mm mm r = mg 5111(cot) with g = 9.81 this2 and a constant angular speed to. The rod is initially horizontal, and the initial conditions for the head are rf) = in} and r143] = on. A) Analytically solve this initial value problem for 'rlft) E) Consider the initial position to be zero, i.e. rIa = ID. Find the initial velocity, v0, that results in a solution; tit}, which displays simple harmonic motionr i.e. a solution that does not tend toward innity. C) Explain why any initial velocity besides the one you found in part B} causes the head to fly off the rod. [1'] Given r(t] displays simple harmonic motion, i.e. part B], nd the minimum required length of the rodr L, as a function of the angular speed; to. E) Suppose a: = 2, graph the solutions t), for the initial conditions given here: r = {i and initial velocities of on = 2.40, 2.45; 2.5, and the initial velocity you found in part B). Use ID i t :1 5