The beam shown in Figure P4.7 has been stiffened by the addition of a spring support. The steel beam is 3 ft long, 1 in thick, and 1 ft wide, and its mass is 3.8 slugs. The mass m is 40 slugs....

The beam shown in Figure P4.7 has been stiffened by the addition of a spring support. The steel beam is 3 ft long, 1 in thick, and 1 ft wide, and its mass is 3.8 slugs. The mass m is 40 slugs. Neglecting the mass of the beam,

a. Compute the spring constant k necessary to reduce the static deflection to one-half its original value before the spring k was added.

b. Compute the natural frequency ω_n
of the combined system.