Solution Found!
(a) Write down the equations of motion (11.2) for the
Chapter 11, Problem 11.9(choose chapter or problem)
(a) Write down the equations of motion (11.2) for the equal-mass carts of Section 11.2 with three identical springs. Show that the change of variables to the normal coordinates 1 = z (xi + x2) and 2 = z (xi x2) leads to uncoupled equations for 1 and 2 (b) Solve for t and 2 and hence write down the general solution for x1 and x2. (Notice how very simple this procedure is, once you have guessed what the normal coordinates are. For a simple symmetric system like this, you can sometimes guess the form of 1 and 2 by considering the symmetry especially once you have some experience working with normal modes.)
Questions & Answers
QUESTION:
(a) Write down the equations of motion (11.2) for the equal-mass carts of Section 11.2 with three identical springs. Show that the change of variables to the normal coordinates 1 = z (xi + x2) and 2 = z (xi x2) leads to uncoupled equations for 1 and 2 (b) Solve for t and 2 and hence write down the general solution for x1 and x2. (Notice how very simple this procedure is, once you have guessed what the normal coordinates are. For a simple symmetric system like this, you can sometimes guess the form of 1 and 2 by considering the symmetry especially once you have some experience working with normal modes.)
ANSWER:Step 1 of 5
(a) With identical masses and springs, the two equations of motion (11.2) are