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, x(0) = 0. Does one get resonance? (b) Using the methods of the characteristic equation and undetermined coefficients, find the general solution of +0.1x + x = sint. 5 (c) Without determining explicit values of the constants c and c in your answer to (b), what can you say about the behavior of the solution for large times? (d) Comment on the effect of damping (e.g. by fixing the hydraulic damp- ing system of a car) on the risk of catastrophic resonance. Use the language of Section 5.17 of the Notes to describe what happens.