Figure 1.  Harmonic excitation of an undamped SDOF system

The equation of motion for this single degree-of-freedom system is:

Because the system is linear and the excitation amplitude u_o and frequency w are constants,  this second-order differential equation can be solved using the Linear System Time Response module. The module input form corresponding to the problem statement is shown in Figure 2.  The calculated results for t = 0 to t = p/4 are plotted in Figure 3 for comparison to Example 4.1 of Craig (Reference 1 below).  Tabulated output of the calculated results for t = 0 to t = 0.2 is shown in Figure 4 for comparison to Example 7.2 of Craig (Reference 1 below).

Figure 2.  Linear System Time Response module input form for SDOF system

Figure 3.  Plot of calculated time response

Figure 4.  Tabulated results