Consider the two-mass, three-spring system whose equations
Chapter 7, Problem 30(choose chapter or problem)
Consider the two-mass, three-spring system whose equations of motion are Eqs. (22) inthe text. Let m1 = 1, m2 = 4/3, k1 = 1, k2 = 3, and k3 = 4/3.(a) As in the text, convert the system to four first order equations of the form y= Ay.Determine the coefficient matrix A.(b) Find the eigenvalues and eigenvectors of A.(c) Write down the general solution of the system.(d) Describe the fundamental modes of vibration. For each fundamental mode drawgraphs of y1 versus t and y2 versus t. Also draw the corresponding trajectories in the y1y3-and y2y4-planes.(e) Consider the initial conditions y(0) = (2, 1, 0, 0)T . Evaluate the arbitrary constants inthe general solution in part (c). What is the period of the motion in this case? Plot graphsof y1 versus t and y2 versus t. Also plot the corresponding trajectories in the y1y3- andy2y4-planes. Be sure you understand how the trajectories are traversed for a full period.(f) Consider other initial conditions of your own choice, and plot graphs similar to thoserequested in part (e).
Unfortunately, we don't have that question answered yet. But you can get it answered in just 5 hours by Logging in or Becoming a subscriber.
Becoming a subscriber
Or look for another answer