(4) Recall from class, it can be shown that the response of a viscously damped SDOF system Fou(t), (with 0 < < 1) to ramp excitation of the form FRamp(t) = Fot u(t), where u(t) is the Heaviside (unit step function), is: XRamp (t) Fo kT 23 - n +e-swnt (25 -cos(wat) + Wn 232-1 Wd sin(w n(wat)] u(t) for zero initial conditions. Consider the excitation in Fig. 9.3. The SDOF system parameters are m = 10 kg, k = 4000 N/m, c20 kg/s. Additionally, the input parameters are Fo = 100 N, T = 1 s. Assume zero initial conditions. i. ii. Derive the response by using the superposition of two ramp response with a proper time shift (a single expression with step functions) and plot it for 0 - 3 s. Derive the response by using the convolution integral (one single expression with step functions) and plot it for 0 - 3 s with the response from Part (i) (Show that your results in Part (i) and (ii) match). +F(t) Fo T Figure 9.3: Excitation for analysis in Problem 4.