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
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
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Please explain all steps clearly and how you solved it. Any help will be much appreciated. The topic is system dynamics. Thank you!
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.
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