hrvatski

Slobodne oscilacije napete žice

We consider the oscillations of a string with length L which oscillates in a medium with resistance proportional with velocity, under instantaneous excitation. We will assume that the excitations is not large enough to cause plastic deformations or braking of the string. This motion is described with the following wave equation: \frac{\partial^2 u}{\partial t^2} = c^2 \frac{\partial^2 u}{\partial x^2} - 2 k^2 \frac{\partial u}{\partial t} , with conditions u(0, t)=u_0, \, \, u(L, t)=u_L, u(x, 0)=\alpha_0, \, \, \frac{\partial u(x, 0)}{\partial t} = v_0 \, The upper equation has been solved depending on tense and length of the string, and type of the medium. In order to solve the upper partial differential equation we have used routines included in Mathematica, so as our own routines. All the obtained results are represented graphically with special attention on the animation of the vibrations.

parcijalne diferencijalne jednad\v{z}be; titranje žice

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