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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Concept explainers

Free Damped Vibrations

Free vibration is a type of vibration in which the external force is removed after giving the initial displacement to a body/system. In other words, in this type of vibration, force is applied at the initial displacement of the system, and after the initial displacement, force is removed, and the system vibrates at the natural frequency.

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A,b, and d

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
IMM
m
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.

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