What would happen to the motion of an oscillating system if the sign of the force term, –kx in Eq. 17-2, were changed?

The motion of a body is said to be periodic if it passes through similar conditions after equal intervals of time. Simple harmonic motion is periodic in nature. In accordance to Hooke’s law, with in elastic limits, tension is proportional to extension from the equilibrium position and always points toward the equilibrium position.
A simple harmonic motion is the motion in which the restoring force (F_x(x)) is proportional to displacement (x) from the mean position and opposes its increase.
So,
F_x(x) = -kx
Here, k is the force constant and x is the displacement of the particle from its equilibrium position.
Thus the oscillation is simple harmonic motion (SHM), if F_x(x) = -kx. But if the sign of the force term, -kx in equation F_x(x) = -kx were changed, then the body will never get back to equilibrium position and continue to move with increasing acceleration.