(16) Three Spring-Coupled Masses

This in turn follows because the dynamical equations

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Unformatted text preview: e dynamical equations are linear.] Let us , arbitrarily set the magnitude of to unity. It follows that the normal mode associated with the normal frequency is (216) Likewise, the normal mode associated with the normal frequency is (217) Finally, the normal mode associated with the normal frequency is (218) The vectors , , and are mutually perpendicular. In other words, they are normal vectors. (Hence, the name ``normal'' mode.) Let . It follows that the most general solution to the problem is (219) where (220) (221) (222) Here, and are constants. Incidentally, we need to introduce the arbitrary ampli...
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