GateWay CC
HOOKE’S LAW
SIMPLE HARMONIC MOTION
PHY111 Physics Lab:
AND
Purpose


To determine the spring constant using experimental data
Te determine the period and frequency of harmonic motion of spring
Theory
Simple harmonic motion is defined as a motion of an object when it moves back and
forth. An example of such an object is spring. When force F is applied to a spring, it
stretches for the distance x from the equilibrium position. The relation between F and x
is:
F  k  x
where k is a constant of proportionality. The negative symbol in this formula indicates
that the direction of the force is opposite to the direction of displacement.
The time to complete one full oscillation is called the period T that can be calculated as:
T  2
m
k
Another term used in harmonic oscillation is frequency – It is the number of oscillations
per unit of time, usually per second. Frequency f is:
1
T
1
f 
2
f 
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k
m
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3/2/2016 9:57:00 PM
GateWay CC
Final term that we analyze in the case of harmonic motion is amplitude. Amplitude is the
maximum distance that the object is displaced from the stationary position.
A typical example of simple harmonic motion is spring. When force (mass on the spring)
is applied on string, the spring will be displaced from the stationary position and will
oscillate up and down. The force supplied by the spring on the hanging mass is
proportional to the displacement. This formula is known as Hooke’s Law.
F kx
Figure 2.
The constant of proportionality k can be found experimentally by applying a known
stretching force on the spring and measuring the amount of displacement.
k
F
x
Once the proportionality constant is found it can be used to calculate the frequency and
the period of oscillation.
The equations provided in this lab manual are based on the fact that the mass of the
spring itself is ignored. If the mass of the spring is considered, the equation will be
modified to take into account the mass of the spring.
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GateWay CC
Procedure
Setup the apparatus as shown in Figure 2.
Figure 3
1. With no mass attached to a spring, record the position of the spring with reference to a
meter stick xo.
2. Hang the mass m = 50 grams on the spiral spring.
3. Calculate the stretching force: F = mg, using g = 9.8 m/s2.
4. Measure and record the new position of the spring with reference to a meter stick xf.
5. Calculate the displacement: x = xf – xo
6. Calculate the spring constant: k 
F
x
7. Calculate the period of oscillation T for each mass on the spring.
8. Calculate the frequency of oscillation f for each mass on the spring
9. Repeat steps 2 through 6 by adding additional 50 g of mass on the spring until the total
mass reaches 400 or 500 grams depending on the type of spring that you use.
10. Repeat steps 2 through 9 using two springs in series.
11. Repeat steps 2 through 9 using two springs in parallel.
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GateWay CC
k
k
k
k
k
M
M
M
Figure 3.
Data Table
Part I: Calculating the spring constant, period and frequency
Objects: Mass hanging on one spring
Mass
Force
Initial
Position
Xo
Kg
N
m
Position
Xf
Displacement
X = Xf - Xo
m
M
Period
Frequency
sec
Hz
Constant
0
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
0.50
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GateWay CC
Part II: Calculating the spring constant, period and freauency
Objects: Mass hanging on two springs in parallel
Mass
Force
Initial
Position
Xo
Kg
N
m
Position
Xf
Displacement
X = Xf - Xo
m
M
Period
Frequency
sec
Hz
Period
Frequency
sec
Hz
Constant
0
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
0.50
Part III: Calculating the spring constant, period and frequency
Objects: Mass hanging on two springs in series
Mass
Force
Initial
Position
Xo
Kg
N
m
Position
Xf
Displacement
X = Xf - Xo
m
m
Constant
0
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
0.50
From the data from three tables calculate the average spring constant for each case – one
spring, two springs in parallel and two springs in series.
The strain potential energy (energy stored while under load) can be calculated by using:
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GateWay CC
EPE 
1
Fx
2
Use this formula to calculate EPDE for a Single Spring, for in Two Springs in Series, and for Two
Springs in Parallel
Part IV: Cumulative table
Arrangement
Spring Constant (Nm-1) Elastic Potential Energy (J)
Single Spring
Two Springs in Series
Two Springs in Parallel
Analysis/Questions
1. Plot a graph of Force (in Newtons) vs. displacement (in meters).
2. Find the slope of the line. What are the units and what does the slope represent?
3. Using your graph, determine the weight of your unknown object from its x. Calculate its mass
(F/g). Determine a % error.
4. Which set ahs the highest EPE, and why?
5. Hooke's Law is expressed as F = -kx. What is the meaning of the negative sign?
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