A spring-mass-damper system oscillating about the horizontal surface is subjected to an external force of F = 300 sin (6)(t), where 300 is in Newtons and 6 is in radians per second. The system has a mass 90 [kg], a damping coefficient of 78 [N ⋅ s/m] and a spring constant of 300 [N⁄m]. The system is both given an initial displacement of 1.2 [m] and an initial velocity of 1.4 [m⁄s]. a. Using Method of Undetermined Coefficients, determine the particular solution for the displacement function. b. Determine the unknown coefficients for the homogeneous solution using the initial conditions (Note: the external force already works at t = 0). c. Determine the position, velocity, and acceleration of the system after 10 seconds.
A spring-mass-damper system oscillating about the horizontal surface is subjected to an external force of F = 300 sin (6)(t), where 300 is in Newtons and 6 is in radians per second. The system has a mass 90 [kg], a damping coefficient of 78 [N ⋅ s/m] and a spring constant of 300 [N⁄m]. The system is both given an initial displacement of 1.2 [m] and an initial velocity of 1.4 [m⁄s]. a. Using Method of Undetermined Coefficients, determine the particular solution for the displacement function. b. Determine the unknown coefficients for the homogeneous solution using the initial conditions (Note: the external force already works at t = 0). c. Determine the position, velocity, and acceleration of the system after 10 seconds.
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
A spring-mass-damper system oscillating about the horizontal surface is subjected to an
external force of F = 300 sin (6)(t), where 300 is in Newtons and 6 is in radians per second. The
system has a mass 90 [kg], a damping coefficient of 78 [N ⋅ s/m] and a spring constant of
300 [N⁄m]. The system is both given an initial displacement of 1.2 [m] and an initial velocity of 1.4
[m⁄s].
a. Using Method of Undetermined Coefficients, determine the particular solution for the
displacement function.
b. Determine the unknown coefficients for the homogeneous solution using the initial
conditions (Note: the external force already works at t = 0).
c. Determine the position, velocity, and acceleration of the system after 10 seconds.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 7 steps with 1 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.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