Answer:
If the amplitude of motion exceeds \[\pm {{x}_{0}},\], then the potential energy would be greater than \[\frac{1}{2}kx_{0}^{2}\] at \[x>{{x}_{0}}.\] So its K.E. \[=\frac{1}{2}kx_{0}^{2}-\frac{1}{2}k{{x}^{2}}\] would be negative. This is impossible. Hence the block cannot go beyond \[x=\pm {{x}_{0}}.\]
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