Exact and steady‐state solutions to sinusoidally excited, half‐infinite chains of harmonic oscillators with one isotopic defect

A half‐infinite chain of spring‐mass oscillators with nearest‐neighbor coupling is excited by a sinusoidal force applied to the mass at the accessible end of the chain. The identical linear springs are massless. Each mass has measure m(m>0) except one, which has measure μm(μ>0). An exact solut...

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Bibliographic Details
Published in:Journal of mathematical physics 1990-08, Vol.31 (8), p.1902-1913
Main Authors: Mokole, E. L., Mullikin, A. L., Sledd, M. B.
Format: Article
Language:English
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Summary:A half‐infinite chain of spring‐mass oscillators with nearest‐neighbor coupling is excited by a sinusoidal force applied to the mass at the accessible end of the chain. The identical linear springs are massless. Each mass has measure m(m>0) except one, which has measure μm(μ>0). An exact solution is given for the initial‐value problem in which all initial velocities and displacements are zero. Behavior of the solution for large t (time) is examined. When the concept of average power supplied by the source to the chain in steady state is meaningful, expressions for average power are deduced.
ISSN:0022-2488
1089-7658
DOI:10.1063/1.528689