Question

A reciprocating pump weighing W-150 lb, is mounted at a middle of a steel plate of thickness 0.5 in., width of 20 in., and clamped along two edges as shown. During operation of pump, the plate is subjected to a harmonic force Ft)-Fo.t) ibl. 0.5 in. Fio),x(t) 100 in. where the amplitude of harmonic force is F俨50 lh and its angular frequency: 62.832 radls Model the system as a simple spring and mass system in the horizontal plane. The mass is m-W/g. and the stiffness of the plate fixed at both ends subjected to a concentrated load 192 EI at its center is K x(t) F(t)-Fo cos(o t) Problem #1 (Resonance) The harmonic force has the angular frequency same as natural frequency of the beam 1. Show the analytic equation for the response x(t) for an undamped system under harmonie force, with initial conditions: x(o) 0:(o) 0 2, Determine the Young modulus E for resonance 3. Simulate the problem using Working Model (mass-spring in horizontal plane). 4. Plot the responsx(t) from Working Model and from Matlab Problem #2 (Beats) For the forcing frequeney o 55 radls slightly different than the natural frequency 1. Show the analytic equation for the response x(t) for an undamped systenm 2. 3. 4. under harmonic force, with initial conditions: x(o)- 0,(o) 0 The period of beating Simulate the problem using Working Model (mass-spring in horizontal plane). Plot the response x(t) from Working Model and from Matlab

Answer 1

Sarution; aomooi Ft)e) mass Cm) 2. Centbe ke 13

0.30833 i ue regar the mass conatiburont Cto0) ю, SO Cos 6.832t Roal

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