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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 U12 =  =  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 U12 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.
 Spring '06
 Shiflett

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