2.7 Logarithmic Decrement
53
2.16 In 5 cycles, the amplitude of a motion is observed to decay from 30 to 0.15 mm.
Calculate the damping ratio ζ.
2.17 The instrument of the figure has mass m = 50 kg and is meant for impact on
a surface. The impact velocity is 10 m/s. Inside mountings have k =5 N/m
and c =1 Ns/mm. Determine the maximum deceleration of the instrument, if
it is assumed that it will not bounce.
Prob. 2.17
2.18 Applying energy principle, determine the natural frequency of the beam of
the figure.
Prob. 2.18
2.19 For a SDF damped system, plot three curves of damping factor versus number
of cycles for amplitude reduction of 25, 50 and 75%.
2.20 Determine the natural frequency of the horizontal vibration of the frame by
Rayleigh’s method, assuming the deflection of the column given by
x = x max ( 1 − cos π y/L)
53
2.16 In 5 cycles, the amplitude of a motion is observed to decay from 30 to 0.15 mm.
Calculate the damping ratio ζ.
2.17 The instrument of the figure has mass m = 50 kg and is meant for impact on
a surface. The impact velocity is 10 m/s. Inside mountings have k =5 N/m
and c =1 Ns/mm. Determine the maximum deceleration of the instrument, if
it is assumed that it will not bounce.
Prob. 2.17
2.18 Applying energy principle, determine the natural frequency of the beam of
the figure.
Prob. 2.18
2.19 For a SDF damped system, plot three curves of damping factor versus number
of cycles for amplitude reduction of 25, 50 and 75%.
2.20 Determine the natural frequency of the horizontal vibration of the frame by
Rayleigh’s method, assuming the deflection of the column given by
x = x max ( 1 − cos π y/L)