Two identical harmonic oscillators (with masses M and natural frequencies w0) are coupled such that by adding to the system a mass m common to both oscillators the equations of motion become

Solve this pair of coupled equation, and obtain the frequencies of the normal modes of the system.

Transcribed Image Text:

*, + (m/M)2 + wzx = 0 äz + (m/M)ä1 + wix2 = 0