Problem 1: Figure 1 represents a simplified diagram of a spring-supported vehicle traveling over a rough road. Determine the equation for the amplitude of W as a function of the speed, and determine the most unfavorable speed.

Problem 2: An electric motor of mass 68 kg is mounted on an isolator block of mass 1200 kg and the natural frequency of the total assembly is 160 cpm with a damping factor of ζ = 0.10 (see Fig. 2). If there is an unbalance in the motor that results in a harmonic force of F = 100 sin 31.4t, determine the amplitude of vibration of the block and the force transmitted to the floor.

Problem 3: For the system shown in Fig. 3, W₁ = 200lb and the absorber weight W₂ = 50lb . If WI is excited by a 2 lb-in. unbalance rotating at 1800 rpm, determine the proper value of the absorber spring k₂. What will be the amplitude of W₂?

Problem 4: Determine in matrix form, the equation of motion of the system shown in Fig. 4 using Newton method (show all the FBD)