A uniform slender rod of length L and mass m is pinned at point "O' and connected to a linearspring of stiffness k as shown in Figure la.i. Determine the relationship that defines stability of the undamped system.ii. A linear dashpot of damping coefficient c is added to the system as shown in Figure 1b.Given the following parameters:L=0.4 m, b=0.1 m, m=1.5 kg, k = 50 N/m and c =100 Ns/m,determine an expression for the response of the system if the initial angular displacementand initial angular velocity are 0 rad and 1.5 rad/s respectively.kkwwwwwLLbCFigure laFigure 1b

Given: L=0.4 mb=0.1 mm=1.5 kgk=50 N/mc=100 N.s/mθ=0 radωo=1.5 rad/s

A uniform slender rod of length L and mass m is pinned at point *O' and connected to a linear spring of stiffness k as shown in Figure la. i. Determine the relationship that defines stability of the undamped system. ii. A linear dashpot of damping coefficient c is added to the system as shown in Figure lb. Given the following parameters: L=0.4 m, b=0.1 m, m=1.5 kg, k = 50 N/m and c = 100 Ns/m, determine an expression for the response of the system if the initial angular displacement and initial angular velocity are 0 rad and 1.5 rad/s respectively. k k ww b b Figure la Figure 1b

A uniform slender rod of length L and mass m is pinned at point *O' and connected to a linear spring of stiffness k as shown in Figure la. i. Determine the relationship that defines stability of the undamped system. ii. A linear dashpot of damping coefficient c is added to the system as shown in Figure lb. Given the following parameters: L=0.4 m, b=0.1 m, m=1.5 kg, k = 50 N/m and c = 100 Ns/m, determine an expression for the response of the system if the initial angular displacement and initial angular velocity are 0 rad and 1.5 rad/s respectively. k k ww b b Figure la Figure 1b

Classical Dynamics of Particles and Systems

5th Edition

ISBN:9780534408961

Author:Stephen T. Thornton, Jerry B. Marion

Publisher:Stephen T. Thornton, Jerry B. Marion

Chapter3: Oscillations

Section: Chapter Questions

Problem 3.12P

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