This assignment requires you to go through the laborious but rewarding process of finding the solution to a second-order differential of the form mx" cx' + kx = Fo cos wt This situation can be envisioned as a mass m connected to a Hooke's Law spring with spring constant k and also to a dashpot with damping constant c. A co-sinusoidal external force Fo is applied to the mass as well, driven at a circular frequency of w. All displacements and the force act along the +x axis. For this assignment, m = 2 kg k = 200 kg*s c = 2 kg*s-1 Fo=100 N w = 9 rad*s1 Initial conditions: x(0) = 0 m x'(0) = 0 m*s1 Assignment 1. Find the transient / complementary solution in the form x(t) = ept (c cos wt + C sin wt), where p and w are numerical values. Do not yet solve for C1 and C2. 2. Find the steady periodic / particular solution in the form xp (t) = C cos(wt - ), where C and a are numerical values. 3. State the general solution of the differential equation. 4. Using the initial conditions, determine and write the solution in the form x(t) = - Ce cos(wt ac) + C cos(wt - ), where C. and ac are values determined from the initial conditions and C and a were determined in #2. 5. Make an Excel table of the form at right, where all rows between 0.6 and 10 are filled in 0.1 s steps. Add spreadsheet formulae for each time under each type of solution: the particular, the complete, and the complementary. Then plot an Excel x, y chart with solid lines between points but no points drawn. Discussion 5 t xp(t) x(t) xc(t) 0 0.1 0.2 0.3 0.4 0.5 0.6 10 6. Make a second Excel table of the form at right, where all rows between 3 and 20 are filled in 0.5 ssteps. Add spreadsheet formulae for each circular frequency under the amplitude of the particular solution. Then plot an Excel x, y chart with solid lines between points but no points drawn. Where does practical resonance occur? Page 1 of 2 C(w) 0 0.5 1 1.5 2 2.5 3 20