The single degree of freedom system shown in Figure 3 is at its undeformed position. The SDOF system consists of a rigid beam that is massless. The rigid beam has a pinned (i.e., zero moment) connection to the wall (left end) and it supports a mass m on its right end. The rigid beam is supported by two springs. Both springs have the same stiffness k. The first spring is located at distance L/4 from the left support, where Lis the length of the rigid beam. The second spring is located at distance L from the left support. Rigid, Massless Beam with pin end k m u(t) Figure 3: Single-degree-of-freedom system in Problem 3. Please compute the following: (a) Find the expression of the effective stiffness of the SDOF system (b) Derive the equation of motion of the mass m. (c) Find the expression of the expression of its natural period.

The single degree of freedom system shown in Figure 3 is at its undeformed position. The SDOF system consists of a rigid beam that is massless. The rigid beam has a pinned (i.e., zero moment) connection to the wall (left end) and it supports a mass m on its right end. The rigid beam is supported by two springs. Both springs have the same stiffness k. The first spring is located at distance L/4 from the left support, where Lis the length of the rigid beam. The second spring is located at distance L from the left support. Rigid, Massless Beam with pin end k m u(t) Figure 3: Single-degree-of-freedom system in Problem 3. Please compute the following: (a) Find the expression of the effective stiffness of the SDOF system (b) Derive the equation of motion of the mass m. (c) Find the expression of the expression of its natural period.

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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