
12-34 Mathematical Methods
12.13.5 One-dimensional Wave
Equation
Consider the vibrations of an elastic string placed
along the x-axis, stretched to length l between two
fi xed points x = 0 and x = l. First we consider the prob-
lem when there is an initial displacement but no initial
velocity (string released from rest). Next we consider
motion of a string with an initial velocity but no initial
displacement (string given an initial blow, but from its
horizontal stretched position). Finally, we consider the
case of both initial velocity and initial displacement.
12. 13.6 Vibrating String with Zero
Initial Velocity
Consider an elastic string of ...