Answer Happy

- The figure below shows a network of five masses connected by springs arranged in a square. Each mass weighs m = .2 kg, each spring has a stiffness of k 100 N/m, and the springs are unstretched in the configuration shown. If mass i is allowed to move vertically by a small deflection Li, then the equations of motion for this system can be approximated by mö1 = -k(x1 - x2) – k(x1 – x4) – k(x1 – 25 ) më2 = -k(22 – xi) – k(x2 – 23) – k(x2 – 25) më3 = -k(x3 – x2) – k(x3 – x4) – k(x3 – 25) m84 = -k(14 - 23) - k(24-21)-k(44 - 25) më5 = -k(25 – xı) – k(25 – x2) – k(x5 – 33) – k(x5 – x4). =
(b) Use your equations of motion to find the natural frequencies and the mode shapes for the system. (For this problem, you can compute these using Matlab.) (c) Create a plot showing the different mode shapes. (You can select the way of plotting the mode shapes that you think best describes the system's behavior.) 37 im im * 7x2 X5415 2 2 m w m m xz, 4