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Unformatted text preview: n coupled differential equations that we can try to solve. Consider the following trial function: q j t ( ) = a j e i ! t Substituting this function into our differential equation we obtain F j = m !! q j = ! m 2 a j e i t = # d a j ! 1 e i t ! 2 a j e i t + a j + 1 e i t ( ) or d a j " 1 " 2 d " m 2 $ % & ( ) a j + d a j + 1 = The amplitudes a can be complex. Based on the type of motion we expect the system to carry out, we can try to parameterize the amplitude dependence on j in the following way: a j = ae i j " ( ) where a is now a real number. Taking this expression for a j and substituting it into the previous equation we obtain ae ! i d e ! i $ ! 2 d ! m % 2 & ( ) * + + d e i & ( ) * + =...
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This note was uploaded on 01/08/2012 for the course PHY 235 taught by Professor Morgan during the Spring '09 term at SUNY Stony Brook.
 Spring '09
 MORGAN
 Energy, Force, Mass, Potential Energy

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