For Problem 10-5, assume the forced response is given by and derive expressions for the modal masses and stiffnesses. Convince yourself that a bond graph structure similar to Figure XXXXXXXXXXonly...

For Problem 10-5, assume the forced response is given by

and derive expressions for the modal masses and stiffnesses. Convince yourself that a bond graph structure similar to Figure 10.17 (only including the rigid-body mode) is appropriate for this system.

Problem 10-5

The transverse motion of a tightly stretched string is governed by the simple wave equation, identically to the bar in longitudinal motion,

In the figure the boundaries are force free because the attachment points are massless. The boundary conditions are

Assume a separated solution

and derive the frequency equation and mode shapes, including the rigidbody mode.