Problem 1

A mass m is attached at the end of a bar of negligible mass and is made to vibrate in three different configurations as shown in Figures (a), (b) and (c). Find the configuration corresponding to the highest natural frequency. What would you conclude from your findings?

Problem 2

Find the equation of motion of the uniform rigid bar OA of length l and mass m shown in the figure.

Note:I_G = ml³/12

Problem 3

A single-degree-of-freedom system consists of a mass of 20 kg and a spring of stiffness of 400 N/m. The amplitudes of successive cycles are found to be 50, 45, 40, 35, .... (mm). Determine the type of damping and the magnitude of the damping force. Assume the velocity of the mass at time zero is zero.

Problem 4

Will the force transmitted to the base of a spring mounted machine decrease with the addition of viscous damping? Explain.

Problem 5

A machine having a mass of 140 kg is mounted as shown on springs having a total stiffness of 45,000 N/m. The damping factor is ξ = 0.30. A harmonic force P = 500 sin 15t (with Pin newtons and t in seconds) acts on the mass.

For the sustained steady-state vibration, determine:

(a) The amplitude of the motion of the machine

(b) Its phase with respect to the exciting force

(c) The transmissibility

(d) The maximum dynamic force transmitted to the foundation

(e) The maximum velocity of the motion