Abstract
One of the basic equations of mathematical physics (for instance function of two independent variables) is the differential equation with partial derivatives of the second order (3). This equation is called the wave equation, and is provided when considering the process of transverse oscillations of wire, longitudinal oscillations of rod, electrical oscillations in a conductor, torsional vibration at waves, etc… The paper shows how to form the equation (3) which is the equation of motion of each point of wire with abscissa x in time t during its oscillation. It is also shown how to determine the equation (3) in the task of electrical oscillations in a conductor. Then equation (3) is determined, and this solution satisfies the boundary and initial conditions.
Highlights
In mathematical physics, implied under a wire is a thin elastic thread
If the wire is taken from its original position and released, or without moving the wire, we provide a speed at its initial points, the wire points will move - the wire starts to oscillate, flickers
When the wire oscillates the deviations of the wire points from the initial position are small, on the Ox axis and are in one plane
Summary
In mathematical physics, implied under a wire is a thin elastic thread. Let the wire of the length l at the initial moment match with O from O to l. The oscillations are determined by the function in u(x,t), which gives the displacement value of the wire points from the abscissa x at the moment t (Fig.[1]). In order to get the equation of motion, it is necessary to equalize the external forces acting on the element with the force of inertia. The required function in u(x, t) should satisfy even boundary conditions that determine what happens at the ends of the wire x=0 and x=1, and the initial conditions describing the position of the wire at the initial moment t=0.
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