Physics II Lab w answers_Part_3

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

This preview shows pages 1–2. Sign up to view the full content.

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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 11/26/2011 for the course PHY 2053 taught by Professor Lind during the Fall '09 term at FSU.

### Page1 / 2

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

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online