Work, Energy and Power

The potential energy function for a
particle executing linear simple
harmonic motion is given by V(x) =
kx2/2, where k is the force constant
of the oscillator. For k = 0.5 N m-1
,
the graph of V(x) versus x is shown
in Fig. 5.12. Show that a particle of
total energy 1 J moving under this
potential must ‘turn back’ when it
reaches x = ± 2 m.