The car body vertical displacement, y(t), can be approximately modelled as a damped mass-spring system (called car suspension system) using the following differential equation: Car Body Attaches Here Spring and Damper Hub Assembly mcar ·+ b₂ + ky = f(t) dy dt dt² Wheel and Tire k Car body mcar 4 by ↑y (1) f(t) Where y(t) is the vertical displacement, mear is the car mas, b, is the damping coefficient, k is the spring stiffness constant, t is the time, and f(t) is the hight of the street from the ground level as a function of time. Given that m = 1500 (Kg), b₂ = 2000 (N.s/m), and k = 100000 (N/m). Answer the following questions: 3-A) If the street is straight, so the f(t) = 0, determine the general solution of y(t). 3-B) Given the initial conditions y(0) = 2, and y'(0) = 1, determine the particular solution of y(t). 3-C) Use Laplace transform to solve the given differential equation with the same initial conditions given in (3-B).
The car body vertical displacement, y(t), can be approximately modelled as a damped mass-spring system (called car suspension system) using the following differential equation: Car Body Attaches Here Spring and Damper Hub Assembly mcar ·+ b₂ + ky = f(t) dy dt dt² Wheel and Tire k Car body mcar 4 by ↑y (1) f(t) Where y(t) is the vertical displacement, mear is the car mas, b, is the damping coefficient, k is the spring stiffness constant, t is the time, and f(t) is the hight of the street from the ground level as a function of time. Given that m = 1500 (Kg), b₂ = 2000 (N.s/m), and k = 100000 (N/m). Answer the following questions: 3-A) If the street is straight, so the f(t) = 0, determine the general solution of y(t). 3-B) Given the initial conditions y(0) = 2, and y'(0) = 1, determine the particular solution of y(t). 3-C) Use Laplace transform to solve the given differential equation with the same initial conditions given in (3-B).
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Transcribed Image Text:Activity 3:
The car body vertical displacement, y(t), can be approximately modelled as a damped
mass-spring system (called car suspension system) using the following differential
equation:
Car Body Attaches Here
Spring and Damper
Hub Assembly
ННИНЯТ
d²y
+ b₂
dt²
Wheel and Tire
dy
dt
+ ky = f(t)
k
Car
body
mcar
4
bv
y (t)
f(t)
7/1
Where y(t) is the vertical displacement, mear is the car mas, b, is the damping coefficient, k
is the spring stiffness constant, t is the time, and f(t) is the hight of the street from the ground
level as a function of time. Given that m = 1500 (Kg), b₂ = 2000 (N.s/m), and k = 100000
(N/m). Answer the following questions:
(3-A) If the street is straight, so the f(t) = 0, determine the general solution of y(t).
(3-B) Given the initial conditions y(0) = 2, and y'(0) = 1, determine the particular solution of
y(t).
(3-C) Use Laplace transform to solve the given differential equation with the same initial
conditions given in (3-B).
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 5 steps with 26 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
