In Example 13.2, the complementary solution (transient part) was omitted. If transient effects are included, what are

Question:

In Example 13.2, the complementary solution (transient part) was omitted. If transient effects are included, what are the appropriate conditions for over-damped, critically damped, and under damped motion? Find the displacement q(x, t) that results when under damped motion is included in Example 13.2 (assume that the motion is under damped for all normal modes).