Civil engineering is a relatively traditional discipline which mainly contains mathematical, mechanical and structural courses. Teaching practice for extended thoughts training was carried out during courses to achieve comprehensive application of learned knowledge. The paper takes dynamic response of single degree of freedom (SDOF) system, which is common in structures, as an example. This section is the basic content in structural dynamics and seismic design courses. Dynamic equation of SDOF system can be simplified into a second order differential equation. In general case the damping ratio is less than 0.2 and dynamic response of structures can be usually decreased by increasing damping ratio. Extended thoughts training was carried out during teaching process based on this general assumption. During courses, teaching assistant guided students to raise questions, refer to literature and solve problems. The paper discusses the change of structural responses in small damping ratio cases and analyses the relationship between damping ratios and structural responses in critical damping and over damping cases to assist students establish correct understandings of the influence of damping in the dynamic responses of structures.