4.1 Boundary conditions both homogeneous. One end Neumann, other end Dirichlet

4.2 Boundary conditions both homogeneous. One end Neumann, other Dirichlet. Damping present.

4.2 Boundary conditions both homogeneous. One end Neumann, other Dirichlet. Damping present.

Solve,

Boundary conditions,

Initial conditions,

Use

Solution,

Solve,

Boundary conditions,

Initial conditions,

Use Consider three cases for damping,

Solution case (underdamped) .

Solution case (critical damped)

.

Solution case (overdamped damped)

. First mode only overdamped, rest underdamped.