Determine where the object's kinetic energy and potential energy are the same.

An object on a spring slides on a horizontal frictionless surface with simple harmonic motion. Determine where the object's kinetic energy and potential energy are the same. Assume the maximum displacement of the object is A so it oscillates between +A and −A.
x = ± ?

An object on a spring slides on a horizontal friction less surface with simple harmonic motion, which means the total energy of the object is the elastic potential energy stored in the spring plus the kinetic energy of the object. We know the total energy of the object also equals 1/2kA^2
The position(s) where the potential energy and kinetic energy are the same occur where
Etotal = U + K = 2U.