Question 5.18: A Single-Degree-of-Freedom Vehicle Model The mass–spring–dam...
A Single-Degree-of-Freedom Vehicle Model
The mass-spring-damper system shown in Figure 5.101 represents a vehicle traveling on a rough road. Assume that the surface of the road can be approximated as a sine wave z=Z_{0} \sin (\omega t), where Z_{0}=0.01 \mathrm{~m} and \omega=3.5 \mathrm{rad} / \mathrm{s}. The mathematical model of the system is given by an ordinary differential equation
m \ddot{x}+b \dot{x}+k x=b \dot{z}+k z
where m=3000 \mathrm{~kg}, b=2000 \mathrm{~N} \cdot \mathrm{s} / \mathrm{m}, and k=50 \mathrm{kN} / \mathrm{m}.
a. Build a Simulink model of the system based on the mathematical representation and find the displacement output x(t).
b. Convert the ordinary differential equation to a transfer function and repeat Part (a). Assume zero initial conditions.
c. Build a Simscape model of the physical system and find the displacement output x(t).
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