Q3 Figure Q3 shows a spring-mass system composed of three masses suspended vertically by a series of springs. To develop a mathematical model of the spring-mass system, Newton's second law can be employed in conjunction with force balances. For each mass, the Newton's second law can be expressed as: m = Fp-Fy dt? where m is the mass of an object, -is the acceleration of an object, F, is downward force dt? and Fy is upward force. (a) Show that when the system eventually comes to rest (steady state), the displacements of the masses can be expressed as 3kx, - 2kx, = mg ky = m2g k + kx = m3g -2kx, + 3kx, (b) Write the system of linear equations in Q3(a) in complete matrix form. Solve the system of linear equations in Q3(a) using Doolittle method. Given k = 10kg/s2 g = 9.81m/s² , m_ is the first two digits of your matrix number, m_ is (c) the last two digits of your matrix number and "= 2+5.5 M1=20 M2=01
Q3 Figure Q3 shows a spring-mass system composed of three masses suspended vertically by a series of springs. To develop a mathematical model of the spring-mass system, Newton's second law can be employed in conjunction with force balances. For each mass, the Newton's second law can be expressed as: m = Fp-Fy dt? where m is the mass of an object, -is the acceleration of an object, F, is downward force dt? and Fy is upward force. (a) Show that when the system eventually comes to rest (steady state), the displacements of the masses can be expressed as 3kx, - 2kx, = mg ky = m2g k + kx = m3g -2kx, + 3kx, (b) Write the system of linear equations in Q3(a) in complete matrix form. Solve the system of linear equations in Q3(a) using Doolittle method. Given k = 10kg/s2 g = 9.81m/s² , m_ is the first two digits of your matrix number, m_ is (c) the last two digits of your matrix number and "= 2+5.5 M1=20 M2=01
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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![Q3 Figure Q3 shows a spring-mass system composed of three masses suspended vertically by a
series of springs. To develop a mathematical model of the spring-mass system, Newton's
second law can be employed in conjunction with force balances. For each mass, the Newton's
second law can be expressed as:
d'x
- = F,- Fy
m
dt?
4* is the acceleration of an object, E, is downward force
dt?
where m is the mass of an object,
and Fy is upward force.
(a)
Show that when the system eventually comes to rest (steady state), the displacements
of the masses can be expressed as
3kx,
2kx,
-2kx, + 3kx,
= mg
ky, + ky3
(b)
Write the system of linear equations in Q3(a) in complete matrix form.
(c)
Solve the system of linear equations in Q3(a) using Doolittle method. Given
k = 10kg/s2 g = 9.81m/s² , m is the first two digits of your matrix number, m is
2
m2
the last two digits of your matrix number and "
+ 5.5 .
M1=20
M2=01](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F97b97130-a634-4cac-9f87-ae6c8e5858b4%2Fd505382c-85e9-4d35-9dd1-292653b9dd96%2Fa0zewus_processed.png&w=3840&q=75)
Transcribed Image Text:Q3 Figure Q3 shows a spring-mass system composed of three masses suspended vertically by a
series of springs. To develop a mathematical model of the spring-mass system, Newton's
second law can be employed in conjunction with force balances. For each mass, the Newton's
second law can be expressed as:
d'x
- = F,- Fy
m
dt?
4* is the acceleration of an object, E, is downward force
dt?
where m is the mass of an object,
and Fy is upward force.
(a)
Show that when the system eventually comes to rest (steady state), the displacements
of the masses can be expressed as
3kx,
2kx,
-2kx, + 3kx,
= mg
ky, + ky3
(b)
Write the system of linear equations in Q3(a) in complete matrix form.
(c)
Solve the system of linear equations in Q3(a) using Doolittle method. Given
k = 10kg/s2 g = 9.81m/s² , m is the first two digits of your matrix number, m is
2
m2
the last two digits of your matrix number and "
+ 5.5 .
M1=20
M2=01
![k
k
k
m1
m2
k
m2
X2
m3
m3
X3
The system before release
The system after release
Figure Q3
ll
ll
ll](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F97b97130-a634-4cac-9f87-ae6c8e5858b4%2Fd505382c-85e9-4d35-9dd1-292653b9dd96%2Ft5cysm_processed.png&w=3840&q=75)
Transcribed Image Text:k
k
k
m1
m2
k
m2
X2
m3
m3
X3
The system before release
The system after release
Figure Q3
ll
ll
ll
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