Problem $1.(2\mathrm{.}5\%)$ A uniform cantilever beam of total mass $m$ has a concentrated mass $M$

end. Assume that the deflection of the beam can be described as follow:

$y(x,t)=A[(\frac{x}{L}{)}^4-4(\frac{x}{L})+3]sint$

where $A$ is a constant involving the material properties of the post. Determine:

$(1\mathrm{.}5\%)$ The kinetic energy of the beam and concentrated mass $M.$

$(1\mathrm{.}0\%)$ The effective mass of the beam and concentrated mass $M.$

$(1)$