Question

We have two atoms, atom A and atom B. Atom B is at rest, while Atom A is moving at velocity v0 in the x-direction toward Atom B. Instead of the atoms attaching to each other immediately upon contact, we model the force between the atoms as a spring force that follows the hook
law. When atom A reaches position x_A= −? the atoms are linked together
through a spring with spring constant ? and equilibrium length ?. We assume that
the mass of the spring is very small and negligible. The atoms remain connected
along with the spring through the movement ahead

a) We describe the position of the atoms using the coordinates ?_A and ?_B. Write down an expression
for the forces ?_AB and ?_BA from atom A to atom B and vice versa as a function of positions.
Check that the forces have the correct sign. Then write down the differential equations that describe
the motion of atoms A and B, and find the initial conditions. (We're supposed to utilize Hook's Law here: F=-kx).

b) Calculate the maximum and minimum distance between the atoms.

Answer 1