# Short Answer SHM of diatomic molecule

## Homework Statement

Two identical atoms in a diatomic molecule vibrate as harmonic oscillators. However, their center of mass, midway between them, remains at rest.

1)Show that at any instant, the momenta of the atoms relative to the center of mass are p and -p

2)Show that the total kinetic energy K of the two atoms at any instant is the same as that of a single object with mass m/2 with a momentum of magnitude p .

3)If the atoms are not identical but have masses m_1 and m_2, show that the result of part (a) still holds and the single object's mass in part (b) is (m_1)(m_2)/(m_1+m_2). The quantity (m_1)(m_2)/(m_1+m_2) is called the reduced mass of the system.

## Homework Equations

Energy= 1/2mv^2 + 1/2kx^2 = 1/2kA^2
Momentum= p= mv
Period= T = 2pi (m/k)^(1/2)

## The Attempt at a Solution

This is a short answer problem and I really don't know how to go about this for sure. I think that you can assume that it is working like a spring.

1) I don't know how to show any work for number one, but would it be p= -p because there are no external forces acting? They are the same atoms, so they have to have the same mass and velocity and p=mv.

2)For this all I think is that the KE of the single object would be:
1/2(m/2)v^2= 1/2kA^2. This is for the case when x=0, so there is no potential energy from the spring.

3)This I have no idea.

We really haven't been over anything like this in class, so I am not sure what to do. Thanks for any help.