Eastern Mediterranean University
Department of Mechanical Engineering
Laboratory Handout
COURSE: Dynamics of Machinery ME 331
Semester: Fall (2009-2010)
Name of Experiment: Determination of the stiffness of two different springs
Instructor: Assoc. Prof. Dr. Ugur Atikol
Submitted by:
Student No:
Group No:
Date of experiment:
Date of submission:
------------------------------------------------------------------------------------------------------------
EVALUATION
Activity During Experiment & Procedure
30 %
Data , Results & Graphs
35 %
Discussion, Conclusion & Answer to Questions
30 %
Neat and tidy report writing
5%
Overall Mark
Name of evaluator:
OBJECT:
To determine the stiffness (k1 and k2) of two different springs
by two different methods:
a) The static method.
b) The dynamic method.
APPARATUS:
1. Holder
2. Test spring
3. Different masses of known weight
4. Roller, stop watch and hanger with known mass
THEORY:
Static Method:
A static load F (N) applied on the one end of a spring (while the other end is
fixed) is proportional to the extension.
δ (m) of the spring.
Where k is the stiffness of the spring (N/m).
Dynamic Method:
The equation of a free vibrating spring mass system (k, M) is given as
Where
from which one can write
Where T = 1/f and f is the natural frequency of the system (cycles/sec).
Springs Connected in Series:
When two springs (k1 and k2) are connected in series the equation becomes,
where keq is the equivalent stiffness of the two springs. The equation of this
equivalent stiffness can be written as,
PROCEDURE:
Hang up the first spring from the support pin and hook the load
hanger into the lower end of the spring. Then,
Static Loads: By increasing loads to the load hanger and record the
corresponding deflection for each load. Now, repeat the same procedure for
the other spring.
Vibrating Loads: By increasing masses to the load hanger, displace slightly
and release, record the time corresponding to 20 Cycles for each mass. Now,
repeat the same procedure for the second spring.
Springs Connected in Series: Repeat the same procedures implemented in
static and vibrating loading cases.
RESULTS AND CALCULATIONS:
The table below illustrates the results obtained from the static loading and
their graphs of load (y-axis) against extension (x-axis) for both springs.
For the first spring
mg (N)
δ (m)
For the second spring
mg (N)
δ (m)
Table below reveal the results obtained from the vibrating part and their
2
graphs of m (y-axis) against T (x-axis) for both springs.
For the first spring
m (N)
T² (m)
For the second spring
m (N)
T² (m)
The next table demonstrate the results obtained from the springs in series
2
part their graphs of m (y-axis) against T (x-axis) for the two springs in
series.
For the two springs in series
m (N)
T² (m)
CONCLUSIONS:
1) What relation exists between the applied load and the extension in the
static case?
2) Did the springs in the static case behave according to the relation F =
kδ?
3) For the same spring, do both methods (the static and dynamic) give
the same k value?
4) If the graphs drawn do not pass through the origin state why?
5) Does the keq calculated theoretically agree with that obtained from the
graph drawn for the springs in series case of results and calculations?
6) Comment on the results and give suggestions to improve the accuracy
of the experiment.