1. In arriving at the equation describing the motion of a vibrating string, the weight was assumed to be negligible. Include the weight of the string in the derivation and determine the describing equation. Classify the equation.
2. Derive the describing equation for a stretched string subject to gravity loading and viscous drag. Viscous drag per unit length of string may be expressed by c(∂u/∂t); the drag force is proportional to the velocity. Classify the resulting equation.