Final answer:
The question appears to be related to the application of oscillatory motion and trigonometry in Physics, at the high school level, but lacks complete information for a full answer. It involves calculations of circular motion radii, center of mass, and its motion using given equations.
Step-by-step explanation:
The question provided appears to be related to the topic of oscillatory motion and trigonometry, which falls under the subject of Physics, and is typically taught at high school level. Specifically, the student is asked to find information related to the motion of particles, which involves calculating the radii of the circles of motion, the coordinates of the center of mass, and determining if the center of mass moves in a certain way.
To address the student's needs, there would be a series of steps which include applying trigonometric identities and laws to determine the required physical quantities from the given equations of motion for the particles. However, based upon the question provided, there seems to be important information missing that would be needed to give a complete answer.
Detailed calculations would involve using the equations of motion given to derive the radii of the circular paths, the coordinates of the center of mass by considering the mass distribution of the system, and applying principles of dynamics to decide whether the center of mass moves in a predictable pattern or stays stationary. Additionally, knowledge about the motion of particles in physics is relevant because it's often related to questions on temperature, or other quantities like force and energy, which may also involve solving equations involving powers, such as T^4, by taking root calculations using a calculator as suggested.