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EA3: Systems Dynamics
Mechanical Systems
Sridhar Krishnaswamy
22
VI.5 FORCED OSCILLATIONS OF A SPRINGMASS SYSTEM
Let us return to the springmass system.
But now let us suppose that a
force
source
acts at
one end of the mass as shown.
Furthermore let us say that the springmass system is
initially quiescent (spring is unstretched and mass has zero velocity at time zero).
Figure 6.15
: Springmass system with external forcing
State variables: X
=
r
sp
1
v
m
2
It should be easy for you to show that the state equation for this system is now given by:
˙
r
sp
1
˙
v
m
2
=
0
1

K
1
m
2
0
r
sp
1
v
m
2
+
0
F
3
(
t
)
m
2
which I will write as:
˙
X
=
A
X
+
F
where
F
is called the source term.
In prinicple, it should not be any harder to solve the above system of equations using our
MATLAB mfiles, but I will need to modify my rate function file (rate_fn.m) to another
one (frate_fn.m) which can handle the additional source term on the right side.
I have done
this for you.
%EA3
%%
%%Example: Springmasssystem with a harmonic force source
%%
clear all;
close all;
global A F;
%share these with function frate_fn which computes Xdot=AX+F
%%
%%System parameters
K1
=
40;
%element 1  spring
m2
=
10;
%element 2  mass
wf
=
2.0001;
%frequency of force source function F3(t)=F0*sin(wf*t)
F0
=
1;
%force source amplitude
1
2
3
1: K
1
2: m
2
F
3
(t)=F
o
sinw
f
t
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 Fall '08
 KRISHNASWAMY

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