From mechanics of materials it is known that for a simply supported beam of uniform cross section a static load P applied at the center will cause a deflection δA = PL3/48EI, where L is the length of the beam, E is the modulus of elasticity, and I is the moment of inertia of the cross-sectional area of the beam. Knowing that L = 15ft, E = 30 × 106psi, and I = 2 × 10??3 ft4, determine

(a) The equivalent spring constant of the beam,

(b) The frequency of vibration of a 1500-lb block attached to the center of the beam. Neglect the mass of the beam and assume that the load remains in contact with the beam.

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