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Analytical Mech Homework Solutions 29

# Analytical Mech Homework Solutions 29 - 1 T f t = c 2T f t...

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( ) ( ) ( ) 2 2 1 cos cos T T n f t c f t n t dt n T t ω ω = + D ( ) ( ) 2 2 1 sin sin T T n f t n t dt n T t ω ω + , . . ., and 1, n = ± ± 2, ( ) 2 2 1 T T T = D c f t dt Now, due to the equality of terms in n ± : ( ) ( ) ( ) 2 2 2 cos cos T T n f t c f t n t dt n t T ω ω = + D ( ) ( ) 2 2 2 sin sin T T n f t n t dt n T t ω ω + , . . . 1,2 n = ,3, Equations 3.9.9 and 3.9.10 follow directly. 3.21 ( ) in t n n f t c e ω = , ( ) 2 2 1 T in t T n c f t e T ω = dt , and 0, 1, 2, n = ± ± 2 T π ω = so ( ) 2 in t n c f t e π ω ω π ω ω π = dt ( ) 0 0 2 in t in t e dt e d π ω ω ω π ω ω π t = + 0 0 1 1 2 in t in t e e in in π ω ω ω π ω ω π ω ω = 1 1 1 2 in in e e in π π π + = + For n even, e e and the term in brackets is zero.
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