One end of a spring is rigidly fixed. A block attached to the free end of the spring is pulled through a distance `x_(0)`. On releasing the block, its amplitude of motion cannot exceed `+-x_(0)`. Why?

Explanation

When the spring is stretched by `x_(0)` its P.E.
`=(1)/(2)kx_(0)^(2)`
where k is spring constant. At `xgtx_(0)`. PE will be greater than `(1)/(2)kx_(0)^(2).` Therefore , its `KE=((1)/(2)kx_(0)^(2)-(1)/(2)kx^(2))` would be negative, which is not possible. Therefore, amplitude of motino cannot exceed `+-x_(0)`.