A block of mass \(m\) on a horizontal frictionless surface is connected to a horizontal spring. An experimenter measures the magnitude of the restoring force \(F\) exerted by the spring as a function of displacement \(x\) from equilibrium (\(x = 0\)), as shown in the graph. The force increases linearly from \(0\) to \(F_0\) as \(x\) increases from \(0\) to \(x_0\), and remains constant at \(F_0\) for \(x_0 < x \le 2x_0\). The block is pulled to \(x = 2x_0\) and released from rest. Which of the following claims correctly describes the motion and total mechanical energy \(E\) of the oscillator, and provides a valid justification?