The expression for the time to recoil when the spring constant is zero can not be obtained from equation 1-11 because substituting K~0 yields an indeterminate expression. However, the expression can be derived by substituting K=0 in equation 1-8 and solving the resulting differential equation. This gives the relation between recoil distance and lime as:

For the conditions of equation 1-16, K=2 F«v/D, where FttV is the average spring force over the distance D. For the conditions of equation 1-18 Fo—Fftv. Making these substitutions in equations 1-16 and 1-18 gives the following results:

ForFo=0 For K=0

Since that average spring force must be the same in both cases, the time to recoil is greater for the condition when K=() by a factor of e>

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