(Straightforward) Purpose: Discover that a system of two masses can be a central force system even when they are not interacting at all. Practice with center-of-mass coordinates.
Consider two particles of equal mass \(m\). The forces on the particles are \(\vec F_1=0\) and \(\vec F_2=F_0\hat{x}\). If the particles are initially at rest at the origin, find the position, velocity, and acceleration of the center of mass as functions of time. Solve this problem in two ways,