Name:____________________ Student No.:________ ME143 2 nd Long Exam September 6, 2012 1. For the three degree of freedom system shown, derive the equations of motion and express in matrix form. Determine the fundamental frequencies of the system and the mode shapes for each natural frequency for m 1 = m 2 = m 3 = 1 kg and k 1 =k 2 = k 3 = k 4 = 20 N/m. 2. For the two degree of freedom system shown, derive the equations of motion and express in matrix form. Determine the fundamental frequencies of the system and the mode shapes for each natural frequency for m 1 = m 2 = 1 kg and all k = 20 N/m. Find the system response x 1 (t) and x 2 (t) for the following initial conditions: x 1 (0) = 1.5, x 2 (0) = 2, ẋ 1 (t) = 0 and ẋ 2 (t) = 0.
Name:____________________Student No.:________ME143 2nd Long
ExamSeptember 6, 2012
1. For the three degree of freedom system shown, derive the
equations of motion and express in matrix form. Determine the
fundamental frequencies of the system and the mode shapes for each
natural frequency for m1 = m2 = m3 = 1 kg and k1 =k2 = k3 = k4 = 20
N/m.
2. For the two degree of freedom system shown, derive the
equations of motion and express in matrix form. Determine the
fundamental frequencies of the system and the mode shapes for each
natural frequency for m1 = m2 = 1 kg and all k = 20 N/m. Find the
system response x1(t) and x2(t) for the following initial
conditions: x1(0) = 1.5, x2(0) = 2, 1(t) = 0 and 2(t) = 0.
