4. (20 points) As shown in Figure 3, the hoisting system ignores the deformation of the rope and the weight of the sprin

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4 20 Points As Shown In Figure 3 The Hoisting System Ignores The Deformation Of The Rope And The Weight Of The Sprin 1 (179.94 KiB) Viewed 26 times

4. (20 points) As shown in Figure 3, the hoisting system ignores the deformation of the rope and the weight of the spring and guide wheel, where the lumped mass m= (100+26) kg, and the excitation load F(t) is F(t) = A sin(at) + 4₂ cos(@t) (N) Where, A₁-30, A2=40, @ 30rad/s. (1) Determine the natural frequency according to the following conditions: Case 1: k₁=4×10 N/m, k2 =00; Case 2: k₁=k₂=4×105N/m. (2) When considering the mass of the guide wheel connected by the spring2 and ignoring its moment of inertia, where the mass of the guide wheel m= (100+26) kg, and the stiffness of the springs are: k₁=k₂=4×105N/m. Please give the dynamic balance equation. k₁ k₂ m Fig.3