2.7 Logarithmic Decrement
51
Prob. 2.6
2.7 For a SDF system, if m = 10 kg, k = 10 N/m and c = 4 Ns/m, find the damping
factor ζ, the logarithmic decrement and ratio of any two successive amplitudes.
2.8 A SDF system has an undamped natural frequency of 7 rad/s and a damping
factor of 10%. The initial conditions are x 0 = 0 and ˙
x = 0.5 m/s. Determine
the damped natural frequency and the equation of motion for the system.
2.9 A machine mounted on springs and having a damper is shown in the figure.
Find the equation of motion in terms of initial displacements x 0 and initial
velocity ˙
x 0 .
Prob. 2.9
2.10 In Prob. 2.4, it is found that for the horizontal vibration of BC, the maximum
displacement in the positive direction is 0.8 of the preceding maximum
displacement in that direction. Determine the coefficient of viscous damping,
damping ratio and the logarithmic decrement.
2.11 A 0.02 N force produces a constant velocity of 3 cm/s. Find the damping
factor ζ used in a system having a mass 1 kg and spring stiffness 700 N/m.
2.12 Determine effective stiffness of the springs of the figure.
51
Prob. 2.6
2.7 For a SDF system, if m = 10 kg, k = 10 N/m and c = 4 Ns/m, find the damping
factor ζ, the logarithmic decrement and ratio of any two successive amplitudes.
2.8 A SDF system has an undamped natural frequency of 7 rad/s and a damping
factor of 10%. The initial conditions are x 0 = 0 and ˙
x = 0.5 m/s. Determine
the damped natural frequency and the equation of motion for the system.
2.9 A machine mounted on springs and having a damper is shown in the figure.
Find the equation of motion in terms of initial displacements x 0 and initial
velocity ˙
x 0 .
Prob. 2.9
2.10 In Prob. 2.4, it is found that for the horizontal vibration of BC, the maximum
displacement in the positive direction is 0.8 of the preceding maximum
displacement in that direction. Determine the coefficient of viscous damping,
damping ratio and the logarithmic decrement.
2.11 A 0.02 N force produces a constant velocity of 3 cm/s. Find the damping
factor ζ used in a system having a mass 1 kg and spring stiffness 700 N/m.
2.12 Determine effective stiffness of the springs of the figure.