Dynamics_Part29

Then we use the result to determine the nonlinear

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Unformatted text preview: hen, we use the result to determine the nonlinear spring constant, . (a) The work done by the nonlinear spring force as the collar moves from arbitrary Point x1 to another arbitrary Point x2 is x2 U1-2 = - = - x1 k(x - xo ) + (x - xo )3 dx x=x2 x=x1 1 1 k(x - xo )2 + (x - xo )4 2 4 1 1 1 1 = - k(x2 - xo )2 - k(x1 - xo )2 + (x2 - xo )4 - (x2 - xo )4 2 2 4 4 (b) For the problem at hand, we have x2 = 1 R and x1 = 5 R. Thus, with xo = 1 R, 2 2 2 U1-2 1 = - k 2 1 1 R- R 2 2 2 2 4 4 - 1 5 R- R 2 2 1 - 4 1 1 R- R 2 2 - 1 5 R- R 2 2 1 1 = - k 0 - 4R2 - 0 - 16R4 = 2kR2 + 4R4 2 4...
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This note was uploaded on 05/12/2010 for the course AME 301 taught by Professor Shiflett during the Spring '06 term at USC.

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