Biomedical Engineering Reference
In-Depth Information
4
Molecular Mechanics
In Chapter 3, I showed you how to use classical mechanics to model the vibrational motion
of a diatomic molecule. I also explained the shortcomings of this treatment, and hinted at
applications where a quantum mechanical model would be more appropriate. We will deal
specifically with quantum mechanical models in later chapters.
4.1 More About Balls on Springs
It is time to move on to more complicated molecules. I want to start the discussion by
considering the arrangement of balls on springs shown in Figure 4.1.
We assume that the springs each satisfy Hooke's law. I will call the spring constant of
the left-hand spring
k
1
and the spring constant of the right-hand spring
k
2
. The equilibrium
position corresponds to the two masses having
x
coordinates
R
1,e
and
R
2,e
, and we constrain
the motion so that the springs can only move along the
x
axis. The particle masses are
shown in Figure 4.1.
m
1
m
2
Figure 4.1
Two balls, two springs
