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LAB# 15
SPRING CONSTANT AND SIMPLE HARMONIC MOTION (SHM)
Introduction:
Any system that has inertia and elasticity will return to its
original shape after being slightly deformed and, can execute
harmonic motion.
All such systems experience restoring
forces that push or pull them back to their equilibrium position
or configuration.
A mass attached to a vertical spring is one
such system.
In this case the restoring force is proportional to
the masses displacement from equilibrium.
Such a system
executes simple harmonic motion and the restoring force of the
spring follows Hooke’s law,
assuming of course that the displacements from equilibrium
are not too large.
Here the distance
x
is understood to mean
the distance the mass has been displaced from its equilibrium
position.
The quantity
k
is called the spring constant and is a
measure of the strength of the spring.
Once the spring is
manufactured
k
is fixed, it depends on the material of the
spring, the size and shape of its coils, and other physical
properties of the spring.
You should note the negative sign in
Equation (1).
This says that the force due to the spring is
always in a direction opposite to the displacement of the mass
from its equilibrium position, thus the spring force is a linear
restoring force.
Our objectives in this experiment are to
measure the spring constant,
k
, for our spring and to compare
the theoretical prediction for the period of oscillation of the
mass-spring system with direct measurement of the period.
Equipment:
Coil spring, “Lab#15 SHM” software application,
dual range force sensor, motion sensor, platform balance and
stand, LabPro interface, and set of masses with hanger.
Theory:
Applying Newton’s second law to our system, and using
Equation (1) for the force on the mass by the spring it can be
shown that the system will execute simple harmonic motion
with a period given by,
,
2
k
m
T
(2)
where
m
is the mass of the object attached to the end of the spring.
As it turns out, the mass of
the spring itself does affect the motion of the system.
A typical estimate for the effective mass of
,
kx
F
(1)
Figure 1: Equipment for "Spring
Constant and Simple Harmonic
Motion" experiment showing the
force sensor, motion sensor, spring,
and hanging masses.

This
** preview**
has intentionally

the spring is to take 1/3 of its mass.
This makes our theoretical prediction for the period of
motion of our system,
,
)
3
/
(
2
k
M
m
T
S

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