Page 104 - Thomson, William Tyrrell-Theory of Vibration with Applications-Taylor _ Francis (2010)

Chap. 3 Problems 91

3-50 Logarithmic decrement 8 for small damping is equal to 5 = Show that 8 is
related to the specific damping capacity by the equation

3-51 For a system with hysteresis damping, show that the structural damping factor y is
equal to the loss factor at resonance.
3-52 For viscous damping, the complex frequency response can be written as
1
H(r) =
(1 - r^) + i{2(r)
where r = and ( = c/c^^. Show that the plot of H = x iy leads to the
equation

(>’ + 4??) =(4?7)
which cannot be a circle because the center and the radius depend on the frequency
ratio.