Homework Help is Here – Start Your Trial Now!
Engineering
Mechanical Engineering
Figure 1 below depicts the popular Spring-Mass-Damper system in which m is the mass, c represented by the dashpot symbol in the figure is called the damping factor, and k is the spring constant. The Spring-Mass-Damper system is with m = 20 kg, c = 20 Ns/m, k = 4000 px k piny с m Figure 1: The Spring-Mass-Damper system N/m. Moreover, denote by r(t) the displacement of the spring (from its equilibrium position). The system is acted on by a periodic harmonic force F(t)= Fo sin(wt) where Fo and w are the amplitude and frequency of the harmonic force, respectively. Given that Fo= 100 N and w = 20 rad/s. The Spring-Mass-Damper in Figure 1 is modelled by the following ODE: m d²x dx + c + kx dt² dt F(t) = F(t). (1) Assume that x(0) = 0.01 m and da(0) = 0.0. Your duty as an engineer is to analyse this Spring- Mass-Damper system by fulfilling the following requirements: dt a) Establish the spring displacement trajectory r(t) by solving analytically the ODE equation (1) modelling the Spring-Mass-Damper. b) Using the analytical results obtained from part a), plot the displacement x(t) and the rate of change of the displacement (velocity) da(t). Each plot is with a horizontal time axis and a vertical magnitude axis. All the plots are in the interval of 0 ≤t≤ T where T≥ 4. Note that direct copy of plots generated from computers/machines is not accepted.

Figure 1 below depicts the popular Spring-Mass-Damper system in which m is the mass, c represented by the dashpot symbol in the figure is called the damping factor, and k is the spring constant. The Spring-Mass-Damper system is with m = 20 kg, c = 20 Ns/m, k = 4000 px k piny с m Figure 1: The Spring-Mass-Damper system N/m. Moreover, denote by r(t) the displacement of the spring (from its equilibrium position). The system is acted on by a periodic harmonic force F(t)= Fo sin(wt) where Fo and w are the amplitude and frequency of the harmonic force, respectively. Given that Fo= 100 N and w = 20 rad/s. The Spring-Mass-Damper in Figure 1 is modelled by the following ODE: m d²x dx + c + kx dt² dt F(t) = F(t). (1) Assume that x(0) = 0.01 m and da(0) = 0.0. Your duty as an engineer is to analyse this Spring- Mass-Damper system by fulfilling the following requirements: dt a) Establish the spring displacement trajectory r(t) by solving analytically the ODE equation (1) modelling the Spring-Mass-Damper. b) Using the analytical results obtained from part a), plot the displacement x(t) and the rate of change of the displacement (velocity) da(t). Each plot is with a horizontal time axis and a vertical magnitude axis. All the plots are in the interval of 0 ≤t≤ T where T≥ 4. Note that direct copy of plots generated from computers/machines is not accepted.

Elements Of Electromagnetics
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
See similar textbooks
icon
Related questions
Question
100%
Figure 1 below depicts the popular Spring-Mass-Damper system in which m is the mass, c represented by the dashpot symbol in the figure is called the damping factor, and k is the spring constant. The Spring-Mass-Damper system is with m = 20 kg, c = 20 Ns/m, k = 4000 Px k în с Li m Figure 1: The Spring-Mass-Damper system N/m. Moreover, denote by x(t) the displacement of the spring (from its equilibrium position). The system is acted on by a periodic harmonic force F(t) = Fo sin(wt) where Fo and w are the amplitude and frequency of the harmonic force, respectively. Given that Fo= 100 N and w = 20 rad/s. The Spring-Mass-Damper in Figure 1 is modelled by the following ODE: d²x dx m. +c- + kx = F(t). dt² dt F(t) dx (0) dt (1) Assume that x(0) = 0.01 m and = 0.0. Your duty as an engineer is to analyse this Spring- Mass-Damper system by fulfilling the following requirements: a) Establish the spring displacement trajectory x(t) by solving analytically the ODE equation (1) modelling the Spring-Mass-Damper. b) Using the analytical results obtained from part a), plot the displacement x(t) and the rate of change of the displacement (velocity) dr(t). Each plot is with a horizontal time axis and a vertical magnitude axis. All the plots are in the interval of 0 ≤ t ≤7 where 7 ≥ 4. Note that direct copy of plots generated from computers/machines is not accepted.
Transcribed Image Text:Figure 1 below depicts the popular Spring-Mass-Damper system in which m is the mass, c represented by the dashpot symbol in the figure is called the damping factor, and k is the spring constant. The Spring-Mass-Damper system is with m = 20 kg, c = 20 Ns/m, k = 4000 Px k în с Li m Figure 1: The Spring-Mass-Damper system N/m. Moreover, denote by x(t) the displacement of the spring (from its equilibrium position). The system is acted on by a periodic harmonic force F(t) = Fo sin(wt) where Fo and w are the amplitude and frequency of the harmonic force, respectively. Given that Fo= 100 N and w = 20 rad/s. The Spring-Mass-Damper in Figure 1 is modelled by the following ODE: d²x dx m. +c- + kx = F(t). dt² dt F(t) dx (0) dt (1) Assume that x(0) = 0.01 m and = 0.0. Your duty as an engineer is to analyse this Spring- Mass-Damper system by fulfilling the following requirements: a) Establish the spring displacement trajectory x(t) by solving analytically the ODE equation (1) modelling the Spring-Mass-Damper. b) Using the analytical results obtained from part a), plot the displacement x(t) and the rate of change of the displacement (velocity) dr(t). Each plot is with a horizontal time axis and a vertical magnitude axis. All the plots are in the interval of 0 ≤ t ≤7 where 7 ≥ 4. Note that direct copy of plots generated from computers/machines is not accepted.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 1 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Follow-up Questions
Read through expert solutions to related follow-up questions below.
Follow-up Question

Thanks for your work. Can you please repost with pictures or any other way because my computer doesn't display all the solution steps (error showing equation)

 

 

 

Solution
Bartleby Expert
SEE SOLUTION
Knowledge Booster
Conduction
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.
Similar questions
Recommended textbooks for you
Elements Of Electromagnetics
Elements Of Electromagnetics
Mechanical Engineering
ISBN:
9780190698614
Author:
Sadiku, Matthew N. O.
Publisher:
Oxford University Press
Mechanics of Materials (10th Edition)
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:
9780134319650
Author:
Russell C. Hibbeler
Publisher:
PEARSON
Thermodynamics: An Engineering Approach
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:
9781259822674
Author:
Yunus A. Cengel Dr., Michael A. Boles
Publisher:
McGraw-Hill Education
Control Systems Engineering
Control Systems Engineering
Mechanical Engineering
ISBN:
9781118170519
Author:
Norman S. Nise
Publisher:
WILEY
Mechanics of Materials (MindTap Course List)
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:
9781337093347
Author:
Barry J. Goodno, James M. Gere
Publisher:
Cengage Learning
Engineering Mechanics: Statics
Engineering Mechanics: Statics
Mechanical Engineering
ISBN:
9781118807330
Author:
James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:
WILEY
SEE MORE TEXTBOOKS