Using method of averaging this equation can be written as

......................................................................(6.3.20)

The solution of the above equation can be written as

where

(6.3.21)

.....(6.3.22)

Integrating Eq. (6.3.21) and Eq. (6.3.22) one may obtain

...............................................................................................(6.3.23)

Substituting Eq. (6.3.23) in Eq. (6.3.20) the response of the system can be written as

(6.3.24)

Figure 6.3.3: Time response of the system with Coulomb damping.

Here it may be noted that the response of the system decreases linearly. A Matlab code is given below.