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monatomic lattice with a single effective mass as shown in Fig. 2. For the effective monatomic mass-spring lattice system shown in Fig. 2, the equation of motion for the jth unit cell is written as mðÞj eff d2uðÞj dt2 þ k 1ðÞ2uðÞ j uðÞ 1 uðÞþ ¼ 0 (4) Following the harmonic solution, the displacement of the (jþn)th unit cell is.

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