Take, for example, the potential energy from a spring (Example 8.2.2): U(x)=12kx2+C As you recall from Example 8.2.2, to find this function (in one dimen...Take, for example, the potential energy from a spring (Example 8.2.2): U(x)=12kx2+C As you recall from Example 8.2.2, to find this function (in one dimension), we took the x component of the spring force and (effectively) found the negative of its anti-derivative, which we defined as the potential energy function: \[\begin{aligned} F(x) &= -kx\\ U(x) &= -\int F(x) dx = \int (kx) dx = \frac{1}{2}kx^2+C\\ \therefore F(x) &= -\frac{d}{dx}U(x)\end{…
