2. Consider the horizontally vibrating system shown below: m k2 ww K3 K4 m2 ww m3...

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2. Consider the horizontally vibrating system shown below: m k2 ww K3 K4 m2 ww m3 ww x2 x3 to be solved using Modal Analysis as described in Window 4.5 of the text, where ki = 2, k2 = 1, k3 = 1, k4 = 3, m = 10, m = 1, and m3 = 3. Initial conditions are x2(0) = 1 and 1,3(0) 0, and 1,2,3 = 0. = (a) Determine the equations of motion and write them in matrix form. (b) Determine the eigenvalues and eigenvectors using Matlab or other software. (c) Solve for and plot the free response in the physical domain x1(t), x2(t), x3 (t) for several cycles for each mode. 3. Continuing with the system in Problem 2, now apply modal damping for each mode (i = 0.05, and a single force F(t) = Fo sin(wt) acting on m2. Determine the frequency response function for all three masses. Provide force-normalized magnitude plots where the vertical axis is x/Fo. Make plots using log-log axes. Make sure to plot at least one decade below the lowest resonance frequency and one decade above the highest resonance frequency. 2. Consider the horizontally vibrating system shown below: m k2 ww K3 K4 m2 ww m3 ww x2 x3 to be solved using Modal Analysis as described in Window 4.5 of the text, where ki = 2, k2 = 1, k3 = 1, k4 = 3, m = 10, m = 1, and m3 = 3. Initial conditions are x2(0) = 1 and 1,3(0) 0, and 1,2,3 = 0. = (a) Determine the equations of motion and write them in matrix form. (b) Determine the eigenvalues and eigenvectors using Matlab or other software. (c) Solve for and plot the free response in the physical domain x1(t), x2(t), x3 (t) for several cycles for each mode. 3. Continuing with the system in Problem 2, now apply modal damping for each mode (i = 0.05, and a single force F(t) = Fo sin(wt) acting on m2. Determine the frequency response function for all three masses. Provide force-normalized magnitude plots where the vertical axis is x/Fo. Make plots using log-log axes. Make sure to plot at least one decade below the lowest resonance frequency and one decade above the highest resonance frequency.