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## Homework Statement

Euler-Bernoulli beam with a lumped mass at x=L, simply supported at x=0 and x=L/2. The beam has a linear initial velocity profile v(x) = w*x.

## Homework Equations

BCs

Y(0)=0

y''(0)=0

Y(L/2)=0

Y'''(L)+M/m*beta*Y(L)=0

## The Attempt at a Solution

I can solve the simply supported case, and I can solve the cantilever with tip mass case by separation of variables and eigenfunction expansions. Can this problem be solved in a similar way? When I go at it in a straight forward manner, I only get a single eigenvalue at zero.