Page 63 - Thomson, William Tyrrell-Theory of Vibration with Applications-Taylor _ Francis (2010)

50 Free Vibration Chap. 2

2-59 The equation of motion for the system of Fig. P2-59 with Coulomb damping can be
written as
mx kx = ¡iF sgn ( i)
where sg n (i)= ±1 (i.e., sgn(i) = +1 when x is negative and -1 when i is
positive). The general solution to this equation is
x(t) = A sin + B cos (o^t
iiF .
-h -p sgn(.r)
Evaluate the constants A and B if the motion is started with the initial conditions
jc(0) = Xqand i(0) = 0.

k
I ->VWV-
Figure P2-59.