Homework Help is Here – Start Your Trial Now!
Engineering
Mechanical Engineering
A representation of a vehicle's suspension suitable for modeling the bounce and pitch motions is shown in the figure, which is a side view of the vehicle's body showing the front and rear suspensions. Assume that the car's motion is constrained to a vertical translation x of the mass center and rotation 0 about a single axis that is perpendicular to the page. The body's mass is m and its moment of inertia about the mass center is IG x and 0 are the displacements from the equilibrium position corresponding to y1 = y2 = 0. The displacements, y1(t) and y2(t), are the inputs to the system and they will be specified based on the vehicle's speed and the road surface profile. k2 Front Road surface Rear k y2 If the damping in the suspension is considered small enough that it can be neglected, what will be the expected behavior of the vehicle? a. Derive the dynamic equations for the bounce motion x and pitch motion 0. Assume that x and e are smalI. b. Write the system in state variable form if the state variables are: X = System Parameter values: k1 = 1100 Ib/ft, k2 = 1525 Ib/ft, L1= 4.8 ft, L2 = 3.6 ft, m = 50 slugs, and IG = 1000 slug-ft2.

A representation of a vehicle's suspension suitable for modeling the bounce and pitch motions is shown in the figure, which is a side view of the vehicle's body showing the front and rear suspensions. Assume that the car's motion is constrained to a vertical translation x of the mass center and rotation 0 about a single axis that is perpendicular to the page. The body's mass is m and its moment of inertia about the mass center is IG x and 0 are the displacements from the equilibrium position corresponding to y1 = y2 = 0. The displacements, y1(t) and y2(t), are the inputs to the system and they will be specified based on the vehicle's speed and the road surface profile. k2 Front Road surface Rear k y2 If the damping in the suspension is considered small enough that it can be neglected, what will be the expected behavior of the vehicle? a. Derive the dynamic equations for the bounce motion x and pitch motion 0. Assume that x and e are smalI. b. Write the system in state variable form if the state variables are: X = System Parameter values: k1 = 1100 Ib/ft, k2 = 1525 Ib/ft, L1= 4.8 ft, L2 = 3.6 ft, m = 50 slugs, and IG = 1000 slug-ft2.

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

Please explain all steps clearly and how you solved it. Any help will be much appreciated. The topic is system dynamics. Thank you!

 

A representation of a vehicle's suspension suitable for modeling the bounce and pitch motions is shown in the figure, which is a side view of the vehicle's body showing the front and rear suspensions. Assume that the car's motion is constrained to a vertical translation x of the mass center and rotation 0 about a single axis that is perpendicular to the page. The body's mass is m and its moment of inertia about the mass center is IG- x and 0 are the displacements from the equilibrium position corresponding to y1 = y2 = 0. The displacements, y1(t) and y2(t), are the inputs to the system and they will be specified based on the vehicle's speed and the road surface profile. Front Road surface k2 Rear k1 y2 If the damping in the suspension is considered small enough that it can be neglected, what will be the expected behavior of the vehicle? a. Derive the dynamic equations for the bounce motion x and pitch motion 0. Assume that x and 0 are small. b. Write the system in state variable form if the state variables are: X = System Parameter values: k1 = 1100 lb/ft, k2 = 1525 Ib/ft, L1= 4.8 ft, L2 = 3.6 ft, m = 50 slugs, and IG = 1000 slug-ft2.
Transcribed Image Text:A representation of a vehicle's suspension suitable for modeling the bounce and pitch motions is shown in the figure, which is a side view of the vehicle's body showing the front and rear suspensions. Assume that the car's motion is constrained to a vertical translation x of the mass center and rotation 0 about a single axis that is perpendicular to the page. The body's mass is m and its moment of inertia about the mass center is IG- x and 0 are the displacements from the equilibrium position corresponding to y1 = y2 = 0. The displacements, y1(t) and y2(t), are the inputs to the system and they will be specified based on the vehicle's speed and the road surface profile. Front Road surface k2 Rear k1 y2 If the damping in the suspension is considered small enough that it can be neglected, what will be the expected behavior of the vehicle? a. Derive the dynamic equations for the bounce motion x and pitch motion 0. Assume that x and 0 are small. b. Write the system in state variable form if the state variables are: X = System Parameter values: k1 = 1100 lb/ft, k2 = 1525 Ib/ft, L1= 4.8 ft, L2 = 3.6 ft, m = 50 slugs, and IG = 1000 slug-ft2.
Expert Solution
Step 1

Mechanical Engineering homework question answer, step 1, image 1

trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 5 steps with 5 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Clutches, Brakes, Couplings and Flywheels
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
  • SEE MORE 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