Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §8.6 Force, Work, and Energy, #4 · Calculus · Applications of integrals

A force … stretches a nonlinear spring by

A force $F = 20 x - x^{3}$ stretches a nonlinear spring by $x$ .
(a) What work is required to stretch it from $x = 0$ to $x = 2$ ?
(b) What is its potential energy $V$ at $x = 2$ , if $V (0) = 5$ ?
(c) What is $k = d F / d x$ for a small additional stretch at $x = 2$ ?

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §8.6 Force, Work, and Energy, #4

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