Problem: For this problem, use the water tower. The water tower initially starts at rest and is subject to the pulse excitation shown below that ends at 0.2 sec. Assume the water tower has 5% of critical damping (ζ = 0.05).
a. Using the central difference method and a time step of ?t = 0.02 seconds, find the displacement of the water tower at t = 0.02 and 0.04 seconds.
b. Repeat part (a) using-the Newmark-β method with β = ¼.