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.)
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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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1d59b4e5-8e27-47f3-9d76-c3e04a3682e5%2F0c07aca6-8f88-4f81-a775-89eb6fd29a3b%2Fm8tozdt_processed.png&w=3840&q=75)
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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1d59b4e5-8e27-47f3-9d76-c3e04a3682e5%2F0c07aca6-8f88-4f81-a775-89eb6fd29a3b%2Fknd25zu_processed.png&w=3840&q=75)
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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