ENGR 201: ENGINEERING ANALYSIS II FINITE ELEMENTS Name: April 7, 2023 Use the finite elements method for the hanging cable with a lumped mass shown in the figure below to approximate its response y(x, t) to the initial deflection given as y(x, 0) = yo(x) = 0.1x . Note that the tension in the cable is T(x) = pg(L - x) + mg. Assume that y(x, 0) = 0, L = 1 m, p = 1 kg/m, m = 2 kg, g = 9.81 m/s. Choose one of the following two options: Project Without Bonus Compute y(x, t) for n = 2 and plot y (L/2, t) and y(L, t) vs. time for 10 seconds. Project With Bonus Compute y(x, t) for each of n = 2, 3,4 and plot y(L, t) vs. time for 10 seconds. Plot also w1 (lowest frequency) vs. n to show the convergence of the solution. General Rules Submit a report describing your solution. The report can be hand-written or typed. Computer programs can only be included as supplements. No credit will be given if you submit only the computer program. The project with bonus can be done in groups of up to 2 students. With the successful completion of the project with bonus, you will earn up to 50% of your loss in Test 1 or Test 2 grade, whichever is lower, (your loss is 100 minus your Test 1/2 grade), which will be scaled by your project grade and added to your Test 1/2 grade. -y y (x, t) m