Physics II Lab w answers_Part_3

Physics II Lab w answers_Part_3 - Equations (2) & (3)...

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17 A involves x B and vice – versa. Without the coupling, i.e. in the absence of the spring, x A and x B would be independent oscillations with the natural frequency I L g m / ) ( 0 = . I.3 It is easy to find uncoupled equations describing the normal modes of the system. Define the variables x 1 = x A + x B ; x 2 = x A - x B ----------------------------------------(4) Adding and subtracting eqs(2) and (3) we obtain equations for the variables x 1 and x 2 as 1 2 1 2 x I L g m dt x d ± ² ³ ´ µ - = ---------------------------------------------------- (5) 2 2 2 2 2 2 2 x I l k x I L g m dt x d - ± ² ³ ´ µ - = --------------------------------------------- (6) Note that the equations for x 1 and x 2 are uncoupled .The variables x 1 and x 2 describe independent oscillations and are the two normal modes of the system .The general solution to these equations will be ) cos( ) ( 1 1 1 1 ± + = t A t x ; ) cos( ) ( 2 2 2 1
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This note was uploaded on 11/26/2011 for the course PHY 2053 taught by Professor Lind during the Fall '09 term at FSU.

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Physics II Lab w answers_Part_3 - Equations (2) & (3)...

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