Problem 2 Consider the frictionless rod. i.e. ,8 = I]. The equation ofmotion becomes 612 Ind1:: mwzr = 1rng sin(mt] with g = 9.31 this2 and a constant angular speed to. The rod is initially ho rizontal. and the initial conditions for the bead are rm] = Tu and r'({i] = FD. You will need to write an improved Euler Method system solver to nd r{t) and v[t) A) Numerically solve forr(t] whenn: = 2,1}, = ID, and v0 = 2.4D, 2.45, 2.50. Solve in the time interval t E [0,5]. Use step sizes l]: = 312. Fla, $ and compare your results. Also, compare your best numerical answers with your analytic answers from Problem 1 part E}. E) Numerically solve for Hit] when n: = 2, in;J = ID, and v0 is selected to give simple harmonic motionr i.e. Problem 1 part B. Use small step sizes, e.g. l1 = i. i, i, etc. Solve for the longest time interval , 512 2043 3192 that provides reasonable values for rift). Compare your results to the analytic solution that gives simple harmonic motion. 1|What does this demonstrate about numerical solutions