Consider the underdamped, forced pendulum governed by the ODE d29 d9 E + Tia + (059 = F0 cos(wpt) where2we > 11 >0,wp >0andFe >0. 1) Find a general solution to this ODE. (We already found the complementary solution in class.) 2) Find the solution where 6(0) = 6'(0) = 0. Plot this solution with we = 1, w; = 0.5, Fe = 1 and 1] = 0.01. 3) Plot your solution where 9(0) = 9'(0) = 0 and we = 1, w; = 1, Fe = 1 and 1] = 0.01. 4) Unlike in the model we discussed in class, you should find that the amplitude of this solution does not grow infinitely large, even when we = wp. In real world systems, there is always friction and so 11 is always strictly positive. Does this mean that resonant frequencies (when we = wp) are not a problem in the real world? Explain why/why not. (Hint: Look at the 9 axis in the last answer.)