A combination of simple operations form s a com plex operation. In general, an analog computer
is not used for addition alone or for multiplication by a constant as a single operation. These
can be better perform ed by other means. The value of the computer lie s in its ability to combine
these simple operations into a com plex operation.
An example of a com plex operation is indicated by the circu it shown in Figure 10.
c
ei<>-
e'°—
W W V n
-A/WVW
-AAM/V
-A/WW
1
eo
J
Figure 10
COMPLEX OPERATION
This circu it solves the relationship
—
l
- r r ^ -
RC
J
L Rl
e* ] dt
+ en (o)
where e0 (o) is the output voltage at time t = o (start of problem solution). Am plifier A is used
for sign inversion. It can be omitted if a minus result is acceptable.
Another example of a simple type of problem involving com plex operation is that of an object
falling due to the force of gravity. The acceleration which the body experiences is constant near
the surface of the earth and due to the fo rce exerted on the object by the gravitational field of
the earth. This may be written as an equation,
d * y
_
dt 2 -
where y is the distance the object falls in time t, and g is the acceleration given the object by
the earth's gravitational field. By integrating twice, it is possible to obtain an expression for y
in term s of g and the time t during which the body has fallen. This can easily be set up on the
com puter, using two am plifiers as shown in Figure 11.
AMPLIFIER CONNECTIONS FOR SOLVING "FALLING BODY PROBLEM”
The input voltage e^ is supplied by a suitable power supply and the value of ei is chosen so that
eQ does not exceed the output capacity of am plifier 2. Instructions for setting up this problem
are given on Page 21. It is suggested, however, that the actual setup and solution of the p rob
lem be withheld until the CIRCUIT DESCRIPTION and OPERATION sections of this manual have
been thoroughly reviewed and are generally understood.
Page 11
