Sheet 2 Solution
1. The figure shows a schematic diagram of an automobile syspension system. As the car moves along the
road, the vertical displacements at the tires act as the motion excitation to the automobile suspension
system.The motionof this system consists of a translational motion of the center 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 (b). Assuming that the motion xi at
point P is the input to the system and the vertical motion xo of the body is the output, obtain the transfer
function Xo(s)/Xi(s). (Consider the motion of the body only in the vertical direction) Displacement xo is
measured from the equilibrium position in the absence of input xi.
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2. Obtain the transfer function Y(s)/U(s) of the system shown in Figure. (This system is a simplified
version of an automobile or motorcycle suspension system).
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3. Find the transfer function, G(s)=X2(s)/F(s), for the translational mechanical system shown in Figure.
(5s 2
)
+ 10 X 1 ( s ) − 10 X 2 ( s ) = F ( s )
10F ( s )
1 G( s) =
− 10 X 1 ( s ) + s + 10 = 0 s ( s + 50s + 2)
2
5
4. Write, but do not solve, the equations of motion for the translational mechanical system shown in
Figure.
Writing thee quations of motion,
(s 2 + 2 s + 2) X 1 ( s ) − ( s + 1) X 2 ( s ) − sX 3 ( s ) = 0
− ( s + 1) X 1 ( s ) + (s 2 + 2 s + 1) X 2 ( s ) − sX 3 ( s ) = F ( s )
− sX 1 ( s ) − sX 2 ( s ) − (s 2 + 2 s + 1) X 3 ( s ) = 0
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5. Find the transfer function, G(s)=X2(s)/F(s), for the translational mechanical system shown in Figure.
(s 2
)
+ 3s + 1 X 1 ( s) − (3s + 1)X 2 ( s) = F ( s)
( )
− (3s + 1)X 1 ( s) + s 2 + 4s + 1 X 2 (s) = 0
6.
7.
8.
9. For each of the rotational mechanical systems shown in figure, write, but do not solve, the
equations of motion
J2
ϴ5(S) = rotation of J3
-K2 ϴ3 + [D2 S + (K2 + K3)] ϴ4 - [D2 S + K3] ϴ5 = 0
2
-[D2 S + (K2 + K3)] ϴ4 + [J3 S + D2 S + K3] ϴ5 = 0
