For Example 3.20, plot \(F(t)\) and \(x(t)\) for the case \(\omega_{n}=6 \omega_{T}\). Compare the results with those of Figure 3.50 and discuss. Assume \(T=1 \mathrm{~s}, F_{0}=1 \mathrm{~N}\), \(k=4 \mathrm{~N} / \mathrm{m}\), and \(\zeta=0.1\).

Example 3.20 Response to a Square Wave Using Fourier Series 47 Consider the simple undamped oscillator + wx F(t)/m, where F(t) is the force represented by the square wave function in Figure 3.49. The square wave is the sim- plest of all non-harmonic, periodic functions since the amplitude over each half-period is constant. Solve for the response using the Fourier series representation for F(t), assuming zero initial conditions. Fo F(t) T T -Fo 2 Figure 3.49: A square wave forcing function F (t).