Answer
a) $W=-184J$
b) $W=184J$
c) $W=0J$
Work Step by Step
The total work done by the restoring force is $$\sum W=\frac{1}{2}k(x_0^2-x_f^2)$$
In this exercise, $k=46N/m$
a) $x_0=1m$ and $x_f=3m$
$$\sum W=\frac{1}{2}\times46\Big(1^2-3^2\Big)=-184J$$
b) $x_0=-3m$ and $x_f=1m$ $$\sum W=\frac{1}{2}\times46\Big((-3)^2-1^2\Big)=184J$$
c) $x_0=-3m$ and $x_f=3m$ $$\sum W=\frac{1}{2}\times46\Big((-3)^2-3^2\Big)=0J$$
