| Annotation |
The problem of oscillation of a semi-bounded string at a given initial perturbation ^(x), when the left end of the string moves according to a given law /(t), is considered (t — time). The solution of the problem is obtained in the final form for arbitrary functions ^(x^ Mid f (t). The direct, inverse and reflected from the end of the string wave components that make up the resulting waves are constructed. The influence of the function f (t) on the magnitude of the reflected waves is investigated. For an arbitrary initial perturbation of a string, the law of motion of its end is found, at which the reflected waves disappear. The relevance of the article is determined by a wide range of practical problems related to the vibrations of extended objects (bridges, beams, antennas), when the source of motion is an initial perturbation and a given external force applied to the end of the object. |
| References |
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