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An intersting thing happens when springs systems have no attachments to the outside. Consider the following free system.
Posted: Fri Apr 29, 2022 12:08 pm
by answerhappygod
- An Intersting Thing Happens When Springs Systems Have No Attachments To The Outside Consider The Following Free System 1 (46.77 KiB) Viewed 24 times
An intersting thing happens when springs systems have no attachments to the outside. Consider the following free system. Ecocoyano with spring constants c = Assume down is the positive direction. Write the elongation matrix. -1 1 0 A 0 -1 1 Free Displacements. Because the system is unattached, it is possible to displace the masses without causing any internal force. We will find a (nonzero) displacement vector u so that Ku = A'CAU = 0 (1) Solve ATW O (forward substitution) (2) Solve Ce w (forward substitution) e= (3) Solve Au = e (back substitution). u = We say that u is the null space of the matrix K. All unattached systems have the same u (which you just computed) in their null space, which corresponds to displacing the entire spring system all together.