Note that the representation of the relationship between \(v\) and \(x\) is a timeless map of all the possible states of the system. The two-dimensional "abstract space" of \(\left(x,v\right)\) is known as "phase space" and the system's "trajectory" in this space is a collection of points. Each such point represents a possible state of the system. Thinking about phase space can provide important insight into system behaviour.
1.6 Determine the potential energy \(U\), and the kinetic energy \(K\), as a function of \(x\).