Fixed endpoints select the spatial normal modes , with angular frequencies . Zero initial velocity selects cosine time dependence. Matching the two nonzero initial amplitudes gives
Each term separately satisfies the wave equation and fixed-end boundary conditions. At the prescribed profile is recovered, and differentiating in time gives zero initial velocity.
Figure 1.
Two-mode string motion, sign reversal at half a period and exact recurrence
. Details.

Articles by others on the same topic (0)

There are currently no matching articles.