(b) A mass of 5 kg is dropped onto the end of a cantilever beam with a velocity of 0.5 m/s, as shown in Figure Q1(b). The impact causes vibrations of the mass, which sticks to the beam. The beam is made of steel (E = 210 x 10° N/m²), with a length of 2.1 m long and has a moment of inertia, I = 3 x 106 m². Compute the response of the mass in x(t) = A sin(wt + Ø) by neglecting the beam inertia. Stiffness equation of beam is keq = 3EI natural frequency is w₁ = wnxo is A = √x + (), phase angle is Ø = tan-¹ (*) m amplitude

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Free undamped vibrations

Whenever an object/system displaces in either side of its equilibrium position with the help of an external/internal means, then the object/system moves regularly or randomly on both sides of its equilibrium position. This motion is called vibration. Generally, there are three types of vibration: longitudinal vibration, transverse vibration, and torsional vibration.