ME 375
HOMEWORK #3
Spring 2010
Out:
Jan. 27
th
, 2010
Due: Feb. 3, 2010
PROBLEM 1
:
(40%)
A block of mass m is able to slide on a smooth, horizontal surface. The center of the block O is
connected to ground with two pairs of springdashpot components, as shown in the figure. A
horizontal force f(t) acts at O. Let x and y represent displacements of O and A, respectively, with
the springs being unstretched when x = y = 0, and where A is a massless node connecting the
two pairs of springdashpot components.
a)
Draw individual free body diagrams (FBDs) of the block and of node A. From these FBDs,
derive the equations of motion (EOMs) for the system in terms of the coordinates x(t) and
y(t).
b)
Suppose c
1
= c
2
= 0. Reformulate your EOMs in a) as a single input/output equation with
f(t) as the input and x(t) as the output. Note that with c
1
= c
2
= 0, the two springs are
connected in series. Is the stiffness term in your inputoutput equation consistent with
having these two springs in series? What is the order of this system?
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 Fall '10
 Meckle
 Mass, EOMS, single input/output equation

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