Eigenvalue ratios for vibrating string equations with single-well densities
نویسندگان
چکیده
In this paper, we prove the optimal upper bound ?n?m?(nm)2 of vibrating string?y?=??(x)y, with Dirichlet boundary conditions for single-well densities. The proof is based on inequality ?n(?)?m(?)??n(L)?m(L), L must be a stepfunction. We also same result Sturm-Liouville problems.
منابع مشابه
0 Vibrating the QCD string
The large-distance behaviour of the adiabatic hybrid potentials is studied in the framework of the QCD string model. The calculated spectra are shown to be the result of interplay between potential-type longitudinal and string-type transverse vibrations. General arguments from QCD and lattice data tell that the theory, even quenched in quarks, possesses nontrivial spectrum, so that effective de...
متن کاملEnergy Preserving Schemes for Nonlinear Hamiltonian Systems of Wave Equations . Application to the Vibrating Piano String
The problem of the vibration of a string is well known in its linear form, describing the transversal motion of a string, nevertheless this description does not explain all the observations well enough. Nonlinear coupling between longitudinal and transversal modes seams to better model the piano string, as does for instance the “geometrically exact model” (GEM). This report introduces a general...
متن کاملWave Motion in a Vibrating String
Waves are familiar to us all--such as ocean waves, sound waves, light waves, and waves in a string. Waves may appear to be traveling or appear to be standing still. There are those being transported by a medium as for the ocean or in a guitar string and those that travel best through empty space such as the electromagnetic spectrum including visible light. Waves are a common means by which ener...
متن کاملActive damping of a vibrating string
This paper presents an investigation of active damping of the vertical and horizontal transverse modes of a rigidly-terminated vibrating string. A state-space model that emulates the behavior of the string is introduced, and we explain the theory behind band pass filter control and proportional-integral-derivative (PID) control as applied to a vibrating string. After describing the characterist...
متن کاملThe Dirichlet Problem for the Vibrating String Equation
This note considers the Dirichlet and Neumann type boundary value problem for the simple vibrating string equation. The detailed study for a special boundary is timely in view of certain categorical statements in the recent literature.* The results obtained below indicate how such statements are to be modified.f Of independent interest is the novel procedure, stemming from Lemma 1, for proving ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Differential Equations
سال: 2022
ISSN: ['1090-2732', '0022-0396']
DOI: https://doi.org/10.1016/j.jde.2021.11.006