String Oscillations Equation

Illustrations

Infinite String

Initial Conditions Initial Conditions
as a Plot Oscillations Comments

Rectangular pulse propagation along an infinite string. Pay attention to the splitting of the initial pulse into two rectangular half-waves. The process is not periodic (why?!).

(the plot is built
for the initial speed) Oscillations of an infinite string with zero initial displacement and non-zero initial speed. According to the d'Alembert's formula the solution (the red line) is comprised of two components (blue and green lines) driven in the opposite directions.

Finite String

Initial and Boundary Conditions Initial Conditions
as a Plot Oscillations Comments

The fixed string oscillations constitute the set of standing waves.

The string is fixed on the ends. In an initial moment it is plucked in a point x=a on the distance h from the balance state, then it is released without initial speed.

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Initial Conditions	Initial Conditions as a Plot	Oscillations	Comments
			Rectangular pulse propagation along an infinite string. Pay attention to the splitting of the initial pulse into two rectangular half-waves. The process is not periodic (why?!).
(the plot is built for the initial speed)			Oscillations of an infinite string with zero initial displacement and non-zero initial speed. According to the d'Alembert's formula the solution (the red line) is comprised of two components (blue and green lines) driven in the opposite directions.

Initial and Boundary Conditions	Initial Conditions as a Plot	Oscillations	Comments
			The fixed string oscillations constitute the set of standing waves.
			The string is fixed on the ends. In an initial moment it is plucked in a point x=a on the distance h from the balance state, then it is released without initial speed.