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Obtain the transfer function Y(s)/U(s) of the system shown in Figure 3–21. The input u is a displacement input. (Like the system of Problem A–3–1, this is also a simplified version of an automobile or motorcycle suspension system.)

Obtain the transfer function Y(s)/U(s) of the system shown in Figure 3–21. The input u is a displacement input. (Like the system of Problem A–3–1, this is also a simplified version of an automobile or motorcycle suspension system.)

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
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Obtain the transfer function Y(s)/U(s) of the system shown in Figure 3–21. The input u is a
displacement input. (Like the system of Problem A–3–1, this is also a simplified version of an
automobile or motorcycle suspension system.)

m2 k2 |b ki Figure 3–21 Suspension system. ww
Transcribed Image Text:m2 k2 |b ki Figure 3–21 Suspension system. ww
A-3-1. Figure 3-20(a) shows a schematic diagram of an automobile suspension system. As the car moves along the road, the vertical displacements at the tires act as the motion excitation to the auto- mobile suspension system. The motion of this system consists of a translational motion of the cen- ter of mass and a rotational motion about the center of mass. Mathematical modeling of the complete system is quite complicated. A very simplified version of the suspension system is shown in Figure 3-20(b). Assuming that the motion x, at point P is the input to the system and the vertical motion x, of the body is the output, obtain the transfer function X(s)/x(s). (Consider the motion of the body only in the ver- tical direction.) Displacement x, is measured from the equilibrium position in the absence of input x,- Solution. The equation of motion for the system shown in Figure 3–20(b) is mž, + b(x, – x.) + k(x, – x,) = 0 or mx, + bx, + kx, = bx, + kx, Taking the Laplace transform of this last equation, assuming zero initial conditions, we obtain (ms² + bs + k)X,(s) = (bs + k)X,(s) Hence the transfer function X,(s)/X(s) is given by X,(s) bs + k X(s) ms² + bs + k Center of mass Auto body ile stem; stem. (b) ww ww
Transcribed Image Text:A-3-1. Figure 3-20(a) shows a schematic diagram of an automobile suspension system. As the car moves along the road, the vertical displacements at the tires act as the motion excitation to the auto- mobile suspension system. The motion of this system consists of a translational motion of the cen- ter of mass and a rotational motion about the center of mass. Mathematical modeling of the complete system is quite complicated. A very simplified version of the suspension system is shown in Figure 3-20(b). Assuming that the motion x, at point P is the input to the system and the vertical motion x, of the body is the output, obtain the transfer function X(s)/x(s). (Consider the motion of the body only in the ver- tical direction.) Displacement x, is measured from the equilibrium position in the absence of input x,- Solution. The equation of motion for the system shown in Figure 3–20(b) is mž, + b(x, – x.) + k(x, – x,) = 0 or mx, + bx, + kx, = bx, + kx, Taking the Laplace transform of this last equation, assuming zero initial conditions, we obtain (ms² + bs + k)X,(s) = (bs + k)X,(s) Hence the transfer function X,(s)/X(s) is given by X,(s) bs + k X(s) ms² + bs + k Center of mass Auto body ile stem; stem. (b) ww ww
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