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Consider a safety suspension system designed to protect passengers from an impact in the event of a vehicle accident as shown in the above figure. The suspension system can be modelled as a spring-damper system with spring coefficient k and damping constant c. The passenger can be modelled as a point-mass with mass m and we assume that he/she uses a seatbelt in such a way that his/her body is always connected to the suspension system. We will use the concept of differential equation to predict the behaviour of this suspension system under various conditions.

Consider a safety suspension system designed to protect passengers from an impact in the event of a vehicle accident as shown in the above figure. The suspension system can be modelled as a spring-damper system with spring coefficient k and damping constant c. The passenger can be modelled as a point-mass with mass m and we assume that he/she uses a seatbelt in such a way that his/her body is always connected to the suspension system. We will use the concept of differential equation to predict the behaviour of this suspension system under various conditions.

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
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We assume that the passenger is passive. However, the damping mechanism
is broken in such a way that the suspension only relies on the spring.

g) Modify your answer in point a to account for the broken damper (c=0). h) Write down the characteristic equation of the differential equation in point g! i) Find the roots of the characteristic equation in point h! Use m=100 kg! j) Write down the position of the passengers x(t) if the passenger was initially at x(0) = 0 moving to the left with speed 10 m/s! k) Will the movement of the passenger stabilize over time (x(t) goes to zero)? If not, is it possible to make it stable by modifying the spring constant k? 1) How long would it take for the passenger to pass through his/her initial position 10 times? (Do not count the initial moment when x(0)=0)!
Transcribed Image Text:g) Modify your answer in point a to account for the broken damper (c=0). h) Write down the characteristic equation of the differential equation in point g! i) Find the roots of the characteristic equation in point h! Use m=100 kg! j) Write down the position of the passengers x(t) if the passenger was initially at x(0) = 0 moving to the left with speed 10 m/s! k) Will the movement of the passenger stabilize over time (x(t) goes to zero)? If not, is it possible to make it stable by modifying the spring constant k? 1) How long would it take for the passenger to pass through his/her initial position 10 times? (Do not count the initial moment when x(0)=0)!
Vehicle Suspension System Spring constant k Passenger Fix Base with mass т Damping constant e Consider a safety suspension system designed to protect passengers from an impact in the event of a vehicle accident as shown in the above figure. The suspension system can be modelled as a spring-damper system with spring coefficient k and damping constant c. The passenger can be modelled as a point-mass with mass m and we assume that he/she uses a seatbelt in such a way that his/her body is always connected to the suspension system. We will use the concept of differential equation to predict the behaviour of this suspension system under various conditions.
Transcribed Image Text:Vehicle Suspension System Spring constant k Passenger Fix Base with mass т Damping constant e Consider a safety suspension system designed to protect passengers from an impact in the event of a vehicle accident as shown in the above figure. The suspension system can be modelled as a spring-damper system with spring coefficient k and damping constant c. The passenger can be modelled as a point-mass with mass m and we assume that he/she uses a seatbelt in such a way that his/her body is always connected to the suspension system. We will use the concept of differential equation to predict the behaviour of this suspension system under various conditions.
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