Consider the Lennard-Jones potential between atoms of mass m in a solid material.c) Consider two neighbouring atoms subject to the Lennard-Jones interaction as above. An experimentalist applies an external driving force F = F0cos(ωt) to separate and bring to- gether the atoms. Write down the differential equation describing the motion of the atoms and determine the amplitude of the oscillations as a function of ω0, F0 and m. You may assume that this is after sufficient time so that you may ignore any transient solutions. d). A further interaction is added that introduces friction to the system so that there is now a friction force −c dr dt , where r is the atomic separation. Write down the differential equation and solve it to determine the amplitude in terms of the coefficients in the differential equation. You may assume that this is after sufficient time so that you may ignore any transient solutions.
Consider the Lennard-Jones potential between atoms of mass m in a solid material.c) Consider two neighbouring atoms subject to the Lennard-Jones interaction as above. An
experimentalist applies an external driving force F = F0cos(ωt) to separate and bring to-
gether the atoms.
Write down the differential equation describing the motion of the atoms and determine the
amplitude of the oscillations as a function of ω0, F0 and m. You may assume that this is
after sufficient time so that you may ignore any transient solutions.
d). A further interaction is added that introduces friction to the system so that there is now a
friction force −c
dr
dt , where r is the atomic separation.
Write down the differential equation and solve it to determine the amplitude in terms of the
coefficients in the differential equation. You may assume that this is after sufficient time so
that you may ignore any transient solutions.
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