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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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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbce6c3fc-5060-4ca2-88c7-1140020dfd1b%2F56548f1b-4931-4067-b8b4-99ff5e797d30%2F8ukf5ha_processed.jpeg&w=3840&q=75)
Transcribed Image Text: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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