A seismograph detects vibrations caused by seismic movements. To model this system, assume that the structure has a vibration with an amplitude b and a known frequency w (in radians per second) such that its vertical displacement is given by xB=bsin(wt). This movement of the structure will produce a relative acceleration in the mass m of 2 kg, whose displacement a will be graphed on a roller. A. Draw the free-body diagram and, using the equations of motion for the 2 kg mass, show that the needle of the seismograph satisfies the following differential equation: k = bw² sin(wt) bw² sin(wt) 2w - w²x m m B. Considering that the peak-to-peak displacement graphed by the seismograph is 24 mm and the vibration frequency of the structure is 5 Hz, find the amplitude 6 of the structure's vibration that produces this result if the damping coefficient of the seismograph is c = 10 N\cdots/m. b(w/wn)² sin(wt) √√[1 − (w/w)²]² + [2(Cw/wn)]² k = 1.5 kN/m D 2 kg 24 mm с Structure
A seismograph detects vibrations caused by seismic movements. To model this system, assume that the structure has a vibration with an amplitude b and a known frequency w (in radians per second) such that its vertical displacement is given by xB=bsin(wt). This movement of the structure will produce a relative acceleration in the mass m of 2 kg, whose displacement a will be graphed on a roller. A. Draw the free-body diagram and, using the equations of motion for the 2 kg mass, show that the needle of the seismograph satisfies the following differential equation: k = bw² sin(wt) bw² sin(wt) 2w - w²x m m B. Considering that the peak-to-peak displacement graphed by the seismograph is 24 mm and the vibration frequency of the structure is 5 Hz, find the amplitude 6 of the structure's vibration that produces this result if the damping coefficient of the seismograph is c = 10 N\cdots/m. b(w/wn)² sin(wt) √√[1 − (w/w)²]² + [2(Cw/wn)]² k = 1.5 kN/m D 2 kg 24 mm с Structure
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
Related questions
Question
c=10Ns/m
![A seismograph detects vibrations caused by seismic movements. To model this system, assume that
the structure has a vibration with an amplitude b and a known frequency w (in radians per second)
such that its vertical displacement is given by xB=bsin(wt). This movement of the structure will
produce a relative acceleration in the mass m of 2 kg, whose displacement a will be graphed on a
roller.
A. Draw the free-body diagram and, using the equations of motion for the 2 kg mass, show that the
needle of the seismograph satisfies the following differential equation:
k
= bw² sin(wt)
bw² sin(wt) 2w - w²x
m
m
B. Considering that the peak-to-peak displacement graphed by the seismograph is 24 mm and the
vibration frequency of the structure is 5 Hz, find the amplitude 6 of the structure's vibration that
produces this result if the damping coefficient of the seismograph is c = 10 N\cdots/m.
b(w/wn)² sin(wt)
√√[1 − (w/w)²]² + [2(Cw/wn)]²
k =
1.5 kN/m
D
2 kg
24 mm
с
Structure](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb033ce8c-438c-48a6-b34d-15b70f40072d%2Fa14c1461-b13e-46fb-afad-def586d2328f%2Flikshca_processed.png&w=3840&q=75)
Transcribed Image Text:A seismograph detects vibrations caused by seismic movements. To model this system, assume that
the structure has a vibration with an amplitude b and a known frequency w (in radians per second)
such that its vertical displacement is given by xB=bsin(wt). This movement of the structure will
produce a relative acceleration in the mass m of 2 kg, whose displacement a will be graphed on a
roller.
A. Draw the free-body diagram and, using the equations of motion for the 2 kg mass, show that the
needle of the seismograph satisfies the following differential equation:
k
= bw² sin(wt)
bw² sin(wt) 2w - w²x
m
m
B. Considering that the peak-to-peak displacement graphed by the seismograph is 24 mm and the
vibration frequency of the structure is 5 Hz, find the amplitude 6 of the structure's vibration that
produces this result if the damping coefficient of the seismograph is c = 10 N\cdots/m.
b(w/wn)² sin(wt)
√√[1 − (w/w)²]² + [2(Cw/wn)]²
k =
1.5 kN/m
D
2 kg
24 mm
с
Structure
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 1 images
Recommended textbooks for you
Elements Of Electromagnetics
Mechanical Engineering
ISBN:
9780190698614
Author:
Sadiku, Matthew N. O.
Publisher:
Oxford University Press
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:
9780134319650
Author:
Russell C. Hibbeler
Publisher:
PEARSON
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:
9781259822674
Author:
Yunus A. Cengel Dr., Michael A. Boles
Publisher:
McGraw-Hill Education
Elements Of Electromagnetics
Mechanical Engineering
ISBN:
9780190698614
Author:
Sadiku, Matthew N. O.
Publisher:
Oxford University Press
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:
9780134319650
Author:
Russell C. Hibbeler
Publisher:
PEARSON
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:
9781259822674
Author:
Yunus A. Cengel Dr., Michael A. Boles
Publisher:
McGraw-Hill Education
Control Systems Engineering
Mechanical Engineering
ISBN:
9781118170519
Author:
Norman S. Nise
Publisher:
WILEY
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:
9781337093347
Author:
Barry J. Goodno, James M. Gere
Publisher:
Cengage Learning
Engineering Mechanics: Statics
Mechanical Engineering
ISBN:
9781118807330
Author:
James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:
WILEY