1. Quarter Car Suspension System
Ross Neal

2. I would like to find out the speed in which a car resonates given conditions:
Weight of car: 2500 Kg
Dampening constant: 350 Kg/s
Spring constant: N/m
Statement of Purpose

3. Differential Equation Model
Mẍ=B(ẏ-ẋ)+K(y-x)
Mẍ+Bẋ+Kx=Bẏ+Ky
Model & Free Body Diagram
Differential Equation Model

4. Working out Speed of Car
Translating translational speed of car to frequency of oscillations of road:
Calculate speed of Resonance:
(y:road bumps per meter)
3 mph = 1.4 m/s =
Working out Speed of Car

5. Matlab Simulink Model

6. Animation Implimentation: VPython

7. Animation

8. Given the simple nature of the Model, there can be several improvements:
Add secondary spring-dampener system to simulate inflated rubber tires
Model ½ or full suspension of car
Allow car to tilt with road
Make road less wavy and more bumpy (increase frequency of bumps)
Further Improvements