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Mechanical vibrations (404-1)
HW#1
Due date: Nov 21, 2025
Solve the following problems using Matlab or similar programs:
1. Consider a system with 1-DOF, subjected to dry-friction damping (𝜇𝜇 = 0.3). Find and
plot response of the system considering below data:
𝑚𝑚𝑒𝑒𝑒𝑒 = 10 𝑘𝑘𝑘𝑘
𝑘𝑘𝑒𝑒𝑒𝑒 = 360
𝑁𝑁
𝑚𝑚
𝑥𝑥0 = −1 𝑚𝑚
𝑣𝑣0 = 0
2. Plot the free vibration response of a viscously damped system in terms of different
damping ratio, i.e., 𝜁𝜁 = 0, 0.05, 0.1, 0.2, 0.5, 1, 2.5 & 10. Suppose the following data:
𝑚𝑚𝑒𝑒𝑒𝑒 = 5 𝑘𝑘𝑘𝑘
𝑘𝑘𝑒𝑒𝑒𝑒 = 2000
𝑁𝑁
𝑚𝑚
𝑥𝑥0 = 0.1 𝑚𝑚
𝑣𝑣0 = 0
(Consider suitable time interval between consecutive time steps, e.g., 0.1s)