A stretched string is released from a given initial position. How will it vibrate?
This problem is described in Section 9.6 of Edwards & Penney (1996). The animations are from the Section 9.6 Computing Project, and use the d'Alembert solution method.
The first animation shows the vibration when the initial position function is
f(x) = a [sin x]2with amplitude a = pi/4.
The animation shows one cycle. Use the loop control on your viewer to see continuous motion.
The next animations shows the vibration when the initial position is triangular.
The resulting string positions are trapezoidal. What will happen if we start with a trapezoid?
Why is it different?
Finally, here is a single wave that travels back and forth along the string.
