Analytical Mech Homework Solutions 188

Analytical Mech Homework Solutions 188 - 25 Plugging 2 back...

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25 Plugging 2 ω back into the matrix equation ( ) 2 -= Kq Mq q 0 3 y 3 gives … 12 1 3 1 qq o rx xy =− + = + which can be satisfied in a variety of ways, for example, with 13 1 x x and y y = , etc Pictorially, the three normal modes are … Q -mode: ant-symmetric about y-axis: 1 3 x x and y y == 2 1 Q km mM  =+   Breathing mode: symmetric about y-axis: 1 3 x x and y y = () 2 1 1 2 k M m ωµ Stretching mode: symmetric about y-axis: 1 3 x x and y y = 2 2 1 2 k M m -------------------------------------------------------------------------------------------------- 11.25 (a) Plug each of these functions into the wave equation and it is satisfied! (b) ( ) ( ) it i k i k x Qq q ee e e ωω +∆ =+= + k x 22 k x k x i k k x ee e e
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