b
(b) \(F=-k x\)

\(d w=F \cdot d x\)

\(\int d x=\int_{0}^{x_1}-k x d x\)

\(w=-k \int_{0}^{x_1}xdx\)

\(=-k\left[\frac{x^{2}}{2}\right]_{0}^{x_{1}}\)

\(=-K\left[\frac{x_{1}^{2}}{2}\right]\)

\(w=-\frac{-k x_{1}^{2}}{2}\)

\(w=\frac{-1}{2} k x_{1}^{2}\)

work  done \(=-(w)\)

\(=-\left[\frac{-1}{2} k x_{1}^{2}\right]\)

\(=\frac{1}{2} k x_{1}^{2}\)