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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.

1638_simplified diagram of a spring-supported vehicle.jpg

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.

97_Amplitude of vibration of the block.jpg

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?

2301_Determine the proper value of the absorber spring.jpg

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

1778_Equation of motion of the system.jpg

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