The given equation for displacement, x = cos².wt, does not represent simple harmonic motion. Simple harmonic motion is a type of periodic motion where the displacement of the particle is directly proportional to the force acting on it and is directed towards the equilibrium position. In this case, the displacement, x, is not directly proportional to the force and there is no mention of an equilibrium position.

However, the equation does represent periodic motion. Periodic motion is a type of motion that repeats itself after a certain period of time. In this case, the cosine function has a period of 2π, meaning the displacement will repeat every 2π seconds. So, option 2, "periodic but not simple harmonic," is a valid description of the given motion.

Option 3, "non-periodic," is incorrect because the equation does represent periodic motion.

Option 4, "None of the above," would also be incorrect because the motion is indeed periodic, although not simple harmonic.

In conclusion, option 2 is the correct choice for the given motion.