A construction worker C is standing at the midpoint of a 14 ft long pine board that is sim...

A construction worker C is standing at the midpoint of a 14 ft long pine board that is simply supported. The board is a standard 2 × 12, so its cross-sectional dimensions are as shown. Assuming the worker weighs 180 lb and he flexes his knees once to get the board oscillating, determine his vibration frequency. Neglect the weight of the beam and use the fact that a load P applied to a simply supported beam will deflect the center of the beam PL3/(48EIcs), where L is the length of the beam, E is its modulus of elasticity, and Ics is the area moment of inertia of the cross section of the beam. The elastic modulus of pine is 1.8 × 106 psi.

Figure P9.9