From mechanics of materials it is known that for a cantilever beam of constant cross section a static load P applied at end B will cause a deflection δB = PL3/3EI, 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 = 10 ft, E = 29 x 106 lb/in2, and I = 12.4 in4, determine (a) the equivalent spring constant of the beam, (b) the frequency of vibration of a 520-lb block attached to end B of the same beam.

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A: For solution refer below images.

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A: For solution refer below images.

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Forced undamped vibrations

In mechanical engineering, vibration is expressed as the term that occurs due to an object's backward and forward movement about a point of equilibrium. Generally, there are three types of vibrations which are,