Flag Wave Motion> Show that the kinetic energy of the two-b...
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Show that the kinetic energy of the two-body oscillator of Fig. 17-21a is given by K = src=data:image/png;base64,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 where m is the reduced mass and vx (= v1x - v2x) is the relative velocity. It may help to note that linear momentum is conserved while the system oscillates.
src=data:image/png;base64,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

Radhika Batra , 10 Years ago
Grade 11
anser 1 Answers
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