MEEN 363 Dynamics and Vibrations (Fall) Sample Problems for Exam 2 Prof. Yong-Joe Kim

MEEN 363 Dynamics and Vibrations (Fall)
Sample Problems for
Exam 2 Prof. Yong-Joe
Kim
1. For the system illustrated in Figure 1, 𝑥𝑏(𝑡) = 𝑥0 𝑠𝑖𝑛(𝜔𝑡) is a periodic base
displacement input. For this system, solve the following problems:
(a) Set 𝑥 as the coordinate for the motion of the block and 𝑥 = 0 denotes the unstretched
position of spring 𝑘𝐴. Draw a free body diagram and derive the equation of motion (EOM).
(b) For 𝑘𝐴 = 700 kN/m, 𝑘𝐵 = 300 kN/m, 𝑚 = 60 kg, and 𝑐 = 1.2 kN sec/m, find the
system’s natural frequency (Hz) and damping ratio (ζ).
(c) For 𝑥0 = 14 mm and 𝜔 = 18 Hz, determine the steady-state response of the block 𝑥(𝑡).
(d) Determine the frequency range where the amplitude of the steady-state motion does not
exceed |𝑥𝑚𝑎𝑥| < 10 mm.



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