EML 5060 Homework Set 4 Fall 1999

Page HW Class Topic

17 2.19bgh 2.19e Classification

17 2.20 Classification

17 2.21ac 2.21b Classification: assume u=u(x,y,z)

18 2.25 2.24 Canonical form

18 2.26 Canonical form

18 2.22bfg 2.22d Characteristics

18 2.27ae 2.27d 2D Canonical form

18 2.28cghi 2.28nml 2D Canonical form

98 7.20 7.19 Unsteady heat conduction in a bar

98 7.21 7.22 Unsteady heat conduction in a bar

98 7.26 7.24 Unidirectional viscous flow

99 7.27 7.28 Acoustics in a pipe

99 7.35 7.36 Steady supersonic flow

99 7.37 7.37 Steady heat conduction in a plate

99 7.39 7.38 Potential flow inside a cylinder

00 Unsteady heat conduction in a disk

Also solve the following problem:

Solve the unsteady vibrations of the membrane on a circular drum. The membrane displacement satisfies the wave equation

The boundary condition at the edge is

For initial condition, assume that the membrane is struck at the point r=0.5 and . In other words assume that and that is a delta function at r=0.5 and , so that

for any function .What frequencies will be present in the vibrations, and with what relative strength?