Translate the following into a PDE with boundary conditions.

A horizontal string has lenth . When the string is held in place so the point units from its left end has vertical displacement . The left end of the string is secured to the x-axis, but starting at time the part between its ends is released and its right end is forced to move with vertical displacement . At each point its vertical motion is damped with a force proportional to its instantaneous vertical velocity. Use c as the constant of proportionality, and assume the mass density (mass per unit length) of the string is 1. How to enter the answers.

The PDE is
When the boundary values / initial conditions are:
Left end is secured:
Right end moves vertically:
Initially at rest:
Initial displacement is :

You can earn partial credit on this problem.