Circular motion is defined as the movement of an object along a circular path. In this type of motion, the object travels in a circle at a constant speed. The question asks whether this motion is simple harmonic and/or periodic.

Simple Harmonic Motion (SHM) is a type of motion where the object oscillates back and forth about an equilibrium position. It is characterized by a sinusoidal pattern, where the displacement of the object is directly proportional to the force acting on it and is in the opposite direction of that force.

Periodic motion refers to any motion that repeats itself after a certain time interval. It can be represented by a periodic function, such as a sine or cosine wave.

Now let's analyze the given options:

a) Simple harmonic but not periodic:
This option is incorrect because circular motion does not exhibit the characteristics of SHM. In SHM, the object oscillates back and forth, whereas in circular motion, the object continuously moves along the circular path without oscillating.

b) Periodic and simple harmonic:
This option is incorrect because, as explained above, circular motion is not simple harmonic. Additionally, circular motion is not periodic because the object does not repeat its motion after a fixed time interval. It continuously moves along the circular path without any repetition.

c) Neither periodic nor simple harmonic:
This option is partially correct. Circular motion is neither periodic nor simple harmonic. It does not repeat itself after a fixed time interval, and its motion does not follow a sinusoidal pattern.

d) Periodic but not simple harmonic:
This option is incorrect. Circular motion is not periodic because it does not repeat itself after a fixed time interval. However, it is also not simple harmonic because it does not exhibit the characteristics of SHM.

In conclusion, the correct answer is option 'D' - Circular motion with constant speed is neither periodic nor simple harmonic. Circular motion is continuous and does not exhibit the characteristics of SHM or repeat itself after a fixed time interval.

In a circular motion particle repeats after equal intervals of time. So particle motion on a circular path is periodic but not simple harmonic as it does not execute to and fro motion about a fixed point.