Answer Happy

An intersting thing happens when springs systems have no attachments to the outside. Consider the following free system. Elasmos with spring constants = Assume down is the positive direction Write the elongation matrix -1 1 0 A= 0 -1 1 Free Displacements. Balanced Forces Just as there are certain displacements which cause no force; for this system, many external forces cannot balanced by displacement. We can compute which forces can be balanced investigating when there is a solution to Ku= A'CAU=. (1) Write the LU decomposition for A" ATE (2) Using variables for the components off, divide by L (the left matrix above) using forward substitution. (Winte f1 for fi, and 2 for 12, and f3 for f.) 3 (3) Since the bottom row of U is all O, there will only be a solution to Uu = - (4) Did you really understand this? Write a nonzero force vector which is balanced by displacement. f= If you apply this force to the spring system, the masses won't just move to a new equilibrium position... instead the whole spring system will fly away