Team Assignment Study well the notes on MSD

| August 31, 2017

Question
Team Assignment
Study well the notes on MSD (Mass-Spring-Damper) system.
The molecular bond due to intermolecular forces is flexible. A diatomic molecule like
oxygen (O2), if disturbed, will oscillate to and fro the equilibrium position
( Ro or x = 0 minimum potential energy) approximated by the equation:

µ

d 2x
+ kx = 0
dt 2

Potential Energy V(R)

Where µ is the reduced mass of the system µ = mO2 / 2 and k is the spring constant.

V R = 1 k R – Ro 2 = 1 k x 2
2
2

0

Ro or x = 0
equilibrium

Lennard-Jones 6-12 potential

Ro
mO

mO
R
x = R -Ro

The µ for the Oxygen molecule ( O2 ) is 1.33 x 10 -26 kg and k =1195 N/m. What is the
natural frequency of O2 ?
What will happen to the molecule if it is forced by an external source to vibrate with a
frequency equal to its natural frequency? Explain in detail.
Compare the above results with that of Hydrogen molecule ( H 2 ) µ = 0.83 x 10 -26 kg
and k = 575 N/m, and Nitrogen molecule ( N 2 ) µ = 1.16 x 10 -26 kg and k = 2300 N/m,
Can one conclude that the natural frequency of heavier diatomic molecules is lower than
that of the lighter molecules? Justify your answer.

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