3 Suppressing resonance by damping One lesson to be learned from this project is that one should always keep the hydraulic liquid in a car at a proper level. To see this more explicitly, let us look at a mathematical example where the numbers are kept relatively simple, so the DEs can be solved without too much effort. Problem 5: (a) Using the formula from Section 5.19 in the Notes, find the unique solution of the initial value problem x+x= sint, x(0) = 0, ic(0) = 0. Does one get resonance? (b) Using the methods of the characteristic equation and undetermined coefficients, find the general solution of x + 0.1x + x = sint