Can Elastic Potential Energy Ever Be Negative?

[Joseph Phan]

Homework Statement

Which of the following Graphs BEST illustrates the potential energy vs. time for the system in Figure 1, where t=0 is defined as the time at which the incident box 1st contacts the box on the spring?

My question is why can't the Elastic PE be negative?
The answer is A

Homework Equations

Using Conservation of Energy
1/2mv² = 1/2kx²

The Attempt at a Solution

I Choose C because I knew that at the start, all the energy would be kinetic energy, thus the potential energy must be 0. In addition, I also knew that the graph of a spring must be a sin or cos graph. Once the spring was compressed to the right, it would be positive. However, once the spring travels to the left wouldn't the PE be negative, since the displacement would be negative once it passed the equilibrium point in the spring?

Thanks.

 

[haruspex]

why can't the Elastic PE be negative?

Because energy is never negative, unless you are expressing relative energy levels.

since the displacement would be negative once it passed the equilibrium point in the spring?

The elastic PE is ½kx². If x is negative, does that make that expression negative?