(a) A five-atom linear molecule is simulated by a configuration of masses and ideal spring...

(a) A five-atom linear molecule is simulated by a configuration of masses and ideal springs that looks like the following diagram:

 

All force constants are equal. Find the eigenfrequencies and normal modes for longitudinal vibrations. [Hint: Transform the coordinates ηi to ζi defined by

 

with symmetrical expressions for η2 and η4. The secular determinant will then factor into determinants of lower rank.]

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(b) Solve this problem using computer techniques.