Problem $1\mathrm{.}15$

Determine an expression for the natural frequency of the weight $W$ in each of the cases shown in

Fig. P$1\mathrm{.}15.$ The beams are uniform of cross$-$sectional moment of inertia I and modulus of elasticity

E$.$ Neglect the mass of the beams.

$($b$)$

$($ c $)$

$($d$)$

$W$

$u$