Simple Harmonic Motion-A
Graphic Demonstration
An ordinary kymograph used by biologists to record the contraction cycle of an isolated muscle can be readily adapted to the study of the vibration of a linear diatomic molecule. The system described in the acoompanying figure is analogous to a. diatomic molecule in which one of the atoms (m,) is of infinite mess relative to the other atom (ms). The mass (m,)is attached to a fixed support rod, whereas the mass ( m ~is) attached to a. lightrweight pen assembly which can undergo vertical displacements only. Both of the masses are connected by one or mare coiled springs which represent chemical bonds. The recorder pen is in contact with the paper-lined surface of the rotating drum (d). To record the vibration of our system the mass (m2) is vertically displaced and released. The movement of the recorder pen will trace the resulting vibration an the surface of the rotating drum. Rotation of the drum can be controlled by adjusting the control knob (k). According to Hooke's law, since one of the atoms (m,) is of infinite mass (immobile), the frequency of vibration ( v ) of the system will vary directly as the square root of the spring constant (bond strength in our model), and inversely as the square root of the msss (mn)
" = (&)'/' where k is the force constant of the spring. With the system described it is easy to study the effect of changea in mess and spring constant on the frequency of vibration. The spring constant can be varied quite easily in the following manner. If we connect 4 springs with identical force constants end to end the force constant of the combination will be '/a that of a n individual spring. The frequency of vibration of this system will be n/' that of the single spring example. On the other hand, if the same 4 springs are attached side by side the force constant of the combination will be increased 4-fold, and the frequency of vibration will double. Many other possible uses of the apparatus could be cited, but I will leave this to the ingenuity of the individual student and instructor.
640
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Journol of Chemical Educofion
