# Fixed Rope and Wave Solution

**Classical Mechanics**Level 4

A rope of length 1 is fixed to a wall at \(x=0\) and shaken at the other end so that:

\[x(1,t) = \sin \omega t.\]

Which of the following is a possible displacement of the rope as a function of \(x\) and \(t\) consistent with these boundary conditions, assuming waves the rope propagate with velocity \(v=1\)?