Consider the rocket on a test stand . The nose of the rocket is fixed. The rocket is of length L, constant EA and constant m, mass per unit length. To investigate longitudinal dynamics, the rocket is modeled using axial elements of equal length.
Determine the natural frequencies and the natural modes using a model with nine elements of equal length. Compare the results with those for the three-element model given in the lecture notes as well as the exact solution. Comment on the accuracy of the natural frequencies and the natural modes as the number of elements increases. Note: For convenience, introduce p=((w^2)*(mL^2))/EA