The damping factor, c/c_c, may be determined experimentally by measuring the successive amplitudes of vibrating motion of a system. If two of these maximum displacements can be approximated by x₁ and x₂, as shown in Fig. 22-16, show that In (x₁/x₂) = 2π(c/c_c)/√1 - (c/c_c)². The quantity In (x₁/x₂) is called the logarithmic decrement.

Fig. 22-16

D D X X 41 De (c/2m) X2 12 X3 13 14 Fig. 22-16 X4 -De-(c/2m) - x = D[e (c/2)sin (@at + d)]