The quarter-car model of a vehicle suspension and its free body diagram are shown in Figure 1. In this simpliﬁed model, the masses of the wheel, tire, and axle are neglected, and the mass m represents one-fourth of the vehicle mass. The spring constant k models the elasticity of both the tire and the suspension spring. The damping constant c models the shock absorber. The equilibrium position of m when y=0 is x=0. The road surface displacement y(t) can be derived from the road surface profile and the car’s speed.Draw free body diagram (FBD) and derive the equation of motion of m with y(t) as the input, and obtain the transfer function.If assume:m=300 kgk=20000, 40000, 60000 N/mc=1000, 3000, 5000 N.s/mPlot magnification ratio vs frequency ratio (r=0-4) diagrams for the parameters given above (you can draw the three curves in one diagram for three different k values and do the same for the three c values as well).Use the derived transfer function to model the system and plot the step response for the system by Matlab or Simulink. BodymRoadSuspensionDatum levelFigure 1

Step 1: Step 2: Step 3: Step 4:

Answered: Body m Road Suspension Datum level…

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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The quarter-car model of a vehicle suspension and its free body diagram are shown in Figure 1. In this simpliﬁed model, the masses of the wheel, tire, and axle are neglected, and the mass m represents one-fourth of the vehicle mass. The spring constant k models the elasticity of both the tire and the suspension spring. The damping constant c models the shock absorber. The equilibrium position of m when y=0 is x=0. The road surface displacement y(t) can be derived from the road surface profile and the car’s speed.

Draw free body diagram (FBD) and derive the equation of motion of m with y(t) as the input, and obtain the transfer function.

If assume:

m=300 kg

k=20000, 40000, 60000 N/m

c=1000, 3000, 5000 N.s/m

Plot magnification ratio vs frequency ratio (r=0-4) diagrams for the parameters given above (you can draw the three curves in one diagram for three different k values and do the same for the three c values as well).
Use the derived transfer function to model the system and plot the step response for the system by Matlab or Simulink.