5. A uniform string of length 1, constant density p and tension To has its equilibrium...

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5. A uniform string of length 1, constant density p and tension To has its equilibrium position along the x-axis, with end at x = 0 fixed and the end at x = l free to move (in a plane) perpendicular to the x-axis in such a way that the end of the string remains parallel to the x-axis. If u(x, t) is the transverse displacement of the string at a point x and time t > 0, and released from rest while in the displaced position u(x,0) = hx(1 x), where h> 0 is small, find the subsequent motion of the string. 5. A uniform string of length 1, constant density p and tension To has its equilibrium position along the x-axis, with end at x = 0 fixed and the end at x = l free to move (in a plane) perpendicular to the x-axis in such a way that the end of the string remains parallel to the x-axis. If u(x, t) is the transverse displacement of the string at a point x and time t > 0, and released from rest while in the displaced position u(x,0) = hx(1 x), where h> 0 is small, find the subsequent motion of the string.

Answer rating: 100% (QA)

The problem describes the motion of a string that has been displaced and then released This is a classic problem in the study of waves on a string and can be described by the wave equation which is a ... View the full answer