Solutions to Homework Set 8 1) Pantograph Drag: The cable ...

• cours magistral - matière potentielle : notes

Solutions to Homework Set 8 1) Pantograph Drag: The cable supports waves with dispersion equation ω2 = Ω2 + c2k2. Here c2 = T/ρ. The phase velocity ω/k is always > c, while the group velocity ∂ω/∂k = c2k/ω is always < c. a) We seek a solution of the form y(x−Ut). Plugging this into the equation, we find that the function y(x) must obey −y′′ + γ 2Ω2 c2 y = γ2F T δ(x− Ut).

• wave drag
• rate of change of the component of momentum of the cable
• wave equation with the linear factors
• solutions to the homogeneous equations
• cable
• solution
• dispersion relation
• waves