6. Consider the following model for a mechanical dynamic system consisting of a two linear springs with stiffnesses 1417 N/m and a linear viscous damper with damping 78 N-s/m that are connected between a rigid wall and a 13 kg moving mass (frictionless rollers). 1417 www 78 13 X The initial position and velocity are zero. There is a nonzero input force. F(t)=2834 u(t) N Complete the following. (a) Find the equation of motion and solve for x(t) using Laplace transforms and check using the ilaplace command in MATLABⓇ. (b) Calculate the natural frequency @n, the damping ratio , and the dominant time constant for this system. (c) Using the symbolic manipulation capability in MATLAB®, show that your answer satisfies the initial conditions and solves the original equation of motion. (d) In MATLAB®, plot x(t) for a duration equal to four times the dominant time constant.

6. Consider the following model for a mechanical dynamic system consisting of a two linear springs with stiffnesses 1417 N/m and a linear viscous damper with damping 78 N-s/m that are connected between a rigid wall and a 13 kg moving mass (frictionless rollers). 1417 www 78 13 X The initial position and velocity are zero. There is a nonzero input force. F(t)=2834 u(t) N Complete the following. (a) Find the equation of motion and solve for x(t) using Laplace transforms and check using the ilaplace command in MATLABⓇ. (b) Calculate the natural frequency @n, the damping ratio , and the dominant time constant for this system. (c) Using the symbolic manipulation capability in MATLAB®, show that your answer satisfies the initial conditions and solves the original equation of motion. (d) In MATLAB®, plot x(t) for a duration equal to four times the dominant time constant.

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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