A uniform slender rod of mass M and length L is pinned at one end and attached to a point mass, m through a linear spring of stiffness k as shown in Figure 5. The pinned end of the rod is constrained by a torsional spring of stiffness Kr. Given the following parameters: M=5 kg, L = 1.2 m, K, = 300 Nm/radian, m = 5 kg, k = 1000 N/m, (i) determine the equations of motion of the system (ii) determine the natural frequencies and mode shapes of the system. (iii) If mass m is given a displacement of 3 mm to the right of its equilibrium position and the rod is simultaneously given an initial angular displacement of 10° (7/18 radians) in the anticlockwise direction, determine expressions for the free vibration response of both the rod and mass. - Pinned joint K, Rod of mass, M k w-

A uniform slender rod of mass M and length L is pinned at one end and attached to a point mass, m through a linear spring of stiffness k as shown in Figure 5. The pinned end of the rod is constrained by a torsional spring of stiffness Kr. Given the following parameters: M=5 kg, L = 1.2 m, K, = 300 Nm/radian, m = 5 kg, k = 1000 N/m, (i) determine the equations of motion of the system (ii) determine the natural frequencies and mode shapes of the system. (iii) If mass m is given a displacement of 3 mm to the right of its equilibrium position and the rod is simultaneously given an initial angular displacement of 10° (7/18 radians) in the anticlockwise direction, determine expressions for the free vibration response of both the rod and mass. - Pinned joint K, Rod of mass, M k w-

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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