2.7 Logarithmic Decrement
57
Prob. 2.34
2.35 A mass of 2 kg. is connected to a spring of stiffness 15 N/cm. Determine the
critical damping constant.
2.36 A diver weighing 90 kg. stands at the end of a cantilever diving board of span
1 m. The diver oscillates at a frequency of 2 Hz. What is the flexural rigidity
EI of the diving board?
2.37 A free vibration test is conducted on an empty elevated water tank. A cable
attached to the tank applied a horizontal force of 75 kN and pulls the tank
horizontally by 5 cm. The cable is suddenly cut and the resulting free vibration
is recorded. At the end of 4 complete cycles, the time is 2 s and the amplitude
is 25 mm. From these data compute the following: (a) damping ratio, (b)
natural period of undamped vibration, (c) damping coefficient and (d) number
of cycles required for the displacement amplitude to decrease to 5 mm.
References
1. R.A. Anderson, Fundamentals of Vibration, McMillan Co., New York, 1967.
2. J.M. Biggs, Introduction to Structural Dynamics, McGraw-Hill Book Inc., New York, 1964.
3. R.W. Clough and J. Penzien, Dynamics of Structures, 2nd Edition, McGraw-Hill Book Inc.,
New York, 1993.
4. Roy R. Craig, Jr., Structural Dynamics, John Wiley & Sons, 1981.
5. J.P. Den Hartog, Mechanical Vibrations, Fourth Edition, McGraw-Hill Book Inc., 1956.
6. D.G. Fertis, Dynamics and Vibrations of Structures, John Wiley & Sons, New York, 1973.
7. L.S. Jacobean and R.S. Ayer, Engineering Vibrations, McGraw-Hill Book Inc, 1958.
8. L. Meirovitch, Elements of Vibration Analysis, McGraw-Hill Book Inc., New York, 1975.
9. W.T. Thomson, Theory of Vibration with Applications, Prentice Hall, New Jersey, 1972.
10. M. Paz, Structural Dynamics Theory and Computations, Second Edition, CBS Publication and
Distribution, New Delhi, 1983.
57
Prob. 2.34
2.35 A mass of 2 kg. is connected to a spring of stiffness 15 N/cm. Determine the
critical damping constant.
2.36 A diver weighing 90 kg. stands at the end of a cantilever diving board of span
1 m. The diver oscillates at a frequency of 2 Hz. What is the flexural rigidity
EI of the diving board?
2.37 A free vibration test is conducted on an empty elevated water tank. A cable
attached to the tank applied a horizontal force of 75 kN and pulls the tank
horizontally by 5 cm. The cable is suddenly cut and the resulting free vibration
is recorded. At the end of 4 complete cycles, the time is 2 s and the amplitude
is 25 mm. From these data compute the following: (a) damping ratio, (b)
natural period of undamped vibration, (c) damping coefficient and (d) number
of cycles required for the displacement amplitude to decrease to 5 mm.
References
1. R.A. Anderson, Fundamentals of Vibration, McMillan Co., New York, 1967.
2. J.M. Biggs, Introduction to Structural Dynamics, McGraw-Hill Book Inc., New York, 1964.
3. R.W. Clough and J. Penzien, Dynamics of Structures, 2nd Edition, McGraw-Hill Book Inc.,
New York, 1993.
4. Roy R. Craig, Jr., Structural Dynamics, John Wiley & Sons, 1981.
5. J.P. Den Hartog, Mechanical Vibrations, Fourth Edition, McGraw-Hill Book Inc., 1956.
6. D.G. Fertis, Dynamics and Vibrations of Structures, John Wiley & Sons, New York, 1973.
7. L.S. Jacobean and R.S. Ayer, Engineering Vibrations, McGraw-Hill Book Inc, 1958.
8. L. Meirovitch, Elements of Vibration Analysis, McGraw-Hill Book Inc., New York, 1975.
9. W.T. Thomson, Theory of Vibration with Applications, Prentice Hall, New Jersey, 1972.
10. M. Paz, Structural Dynamics Theory and Computations, Second Edition, CBS Publication and
Distribution, New Delhi, 1983.