In order to transport sensitive equipment a crate is installed inside a truck on damped springs, as shown in Figure 11.23. The suspension system of the truck, including the tyres, may be modelled as a damped spring. The various spring and damper constants are indicated in the figure. The masses of£the crate and truck are M₁ and M₂ respectively and their displacements from equilibrium are respectively x₁(t) and x₂(t). The vertical displacement of the truck as it traverses a bumpy road may be modelled by applying a force u(t) to the truck.
Show that the motion of the crate and truck may be modelled by the differential equations

Using an appropriate software package, such as MATLAB/SIMULINK, the model developed may be used as the basis for simulation studies of various scenarios.

Figure 11.23

Transcribed Image Text:

Mx = K(x-x) + B (x-x) Mx = u(K + K)x + Kx - (B + B)x + BX For the particular case where M = 1, M = 3, K = 2, K = 1, B = 3, B = 2 and u(t) = sin t, and the initial conditions at time t = 0 are x = x = x = 0, * = 2, show that the Laplace transform of x, (t) is X (s) = 18s + 12s + 21s +14 (3s + 145 +15s + 7s + 2)(s + 1)