3 (8 points.) The angle O(t) of a pendulum satisfies the differential equation. 0"(t) + sin(0(t)) = 0 At time t = 0, we push the pendulum from rest, so 0(0) = 0 and #'(0) = v. e(t) 0(0) = 0 The energy of the pendulum at time t is E(t) = 10' (t) 2 - cos(0 (t) ) 3.a (2 points.) Compute dE dt 3.b (2 points.) Using the result of the previous part, explain why E(t) is constant, then find the constant in terms of v only. 3.c (2 points.) Suppose t, is a critical point of the function 0(t). Using the result of the previous part, find cos(0(t.)). 3.d (1 point.) If v = 1, find the maximum value of 0(t) (you do not have to find t). 3.e (1 point.) If v > 2, does 0(t) have any critical point? Explain your