Dawson College - Winter 2023
Teacher : Marie-Pier Neault
Phet Activity on Simple Harmonic Motion
Purpose:
The purpose of this experiment is to study various aspects of simple harmonic motion (SHM)
and to determine the spring constant k of a spring by two different methods.
Apparatus:
Virtual: Spring, masses, spring support, ruler, timer.
Theory:
Part A
A block of mass m is hanging from a spring of spring constant k. If the block has reached
the equilibrium position (i.-e. the mass is at rest), that means the force of the spring
equals the weight of the block. Therefore, one can write that the
magnitude of the gravitation force is equal to the magnitude of the
spring force.
𝐹𝑔 = 𝑚𝑔 = 𝑘∆𝐿 = 𝐹𝑠𝑝𝑟𝑖𝑛𝑔
∆𝐿 =
𝑚𝑔
𝑘
where ∆𝐿is the length from unstretched spring position to the position of the block at rest
which is a absolute value.
Part B
We can define the angular frequency and for a spring in SHM as
𝜔=√
𝑘
𝑚
where
𝑇=
2𝜋
𝑚
= 2𝜋√
𝜔
𝑘
Dawson College - Winter 2023
Teacher : Marie-Pier Neault
Procedure:
For this lab, use the PhET simulation Masses and Springs.
https://phet.colorado.edu/sims/html/masses-and-springs/latest/masses-and-springs_en.html
This simulation mimics a real mass and spring system and allows you to adjust the initial
position, the mass, and the spring constant of the system.
You’ll see four options: “Intro”, “Vectors”, “Energy” and “Lab”, click on the “Lab”
option. Play around with the simulation. You can add mass to the spring and drag the
mass to an arbitrary initial position and release it from rest. You can adjust the mass and
spring constant using the slider bars at the top. Velocity and acceleration vectors can be
selected to be shown, as well as the forms of energy.
Feel free to play around with the simulation. When you are done, click the Reset button at
the bottom right.
Dawson College - Winter 2023
Teacher : Marie-Pier Neault
PART A Determination of the Force Constant of the Spring, k, by a Static Method.
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Click on the “Displacement, Natural Length” check box to display a reference line for the
position of the bottom of the spring. This position represents 𝑥 = 0.
Set the spring Strength Constant to somewhere in the middle of the scale.
Set the amount of Damping to “little”.
Hang a mass from its end, wait a few seconds until the mass stops oscillating
Measure the elongation of the spring ∆𝐿 (the length between the reference line and the
lower end of the spring) by using the ruler provided at the bottom right.
Repeat for a wide range of masses (at least 10). It is recommended that you start with the
highest mass, e.g., 0.300 kg.
Record your data in Table 1 as suggested. The force F which produces this elongation is
the weight of the hanging mass (𝐹 = 𝐹𝑔 = 𝐹𝑠𝑝𝑟𝑖𝑛𝑔 )
PART B Determination of the Force Constant of the Spring, k, by a Dynamic Method.
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Remove any mass you have attached to the spring and replace the ruler on the right. But
keep the spring constant at the same value on the scale (equivalent to keeping the same
spring in the lab).
Set the amount of Damping to “None”.
Suspend a mass from the spring so that it can oscillate in the vertical direction.
Timing: Start the mass oscillating up and down a few centimeters (2 or 3).
Using the stop watch record the time for 10 or more oscillations. (If needed use the Slow
button.)
From this value calculate the period of the motion for this mass
Recording Data: Record the value of the mass m hanging from the spring and your data in
Table 2 as suggested.
Repeat these steps to measure the period T for 8 to 10 different masses.
When You Have Finished:
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You can start your analysis by using the Excel program found on your computer
You do not have Office on your computer? Just sign in to get it online for free: Free
Microsoft Office online, Word, Excel, PowerPoint, formerly Office Online
Dawson College - Winter 2023
Teacher : Marie-Pier Neault
Data
PART A: Determination of the Force Constant of the Spring, k, by the Static Method
Mass
Force
Elongation
Spring constant
m (kg)
F (N)
ΔL (m)
k (𝑁/𝑚)
PART B: Determination of the Force Constant of the Spring, k, by the Dynamic Method
Mass
Mean Period
Mean Period
Spring constant
m (kg)
T (s)
k (𝑁/𝑚)
Squared 𝑇 2 (𝑠 2 )
Dawson College - Winter 2023
Teacher : Marie-Pier Neault
Calculations
1. Using the static method, show your calculation to find the spring constant for your first
data using word - equation.
2. Using the dynamic method, show your calculation to find the
spring constant for your first data word - equation.
Questions
1. Static Method
On Excel graph 𝐹𝑠𝑝 as a function the elongation. By fitting the best line to the data points
and quoting the equation of the best fit on the graph you should be able to get the
measure of the spring constant.
2. Dynamic method
Calculate the average spring constant from the dynamic method.
3. Pourcentage difference
Compare the results for the spring constant obtained from the static with the dynamic
method by calculate the % difference for the spring constants. The percentage difference
is given to only one significant figure.
𝑋−𝑌
× 100 =
𝑋+𝑌
2