Lab #11 Template:
Simple Harmonic Motion of a Linear Oscillator
Score: ______ / 75
Name:
Section #:
Name:
Section #:
Name:
Section #:
Activity 1: Analysis of the Simple Harmonic Motion of a Cart / Spring System (35 pts)
Setting Up the Graphs:
4.
(2 pts) Using the ruler located along the length of the track, estimate the distance from the motion
detector to the closest end of the cart when the cart is at rest in the equilibrium position. Record
this value in the table below.
Distance of Cart from Motion Detector at
Equilibrium (meters)
6.
(2 pts) Notice that the Position vs. Time graph does not oscillate around the x-axis of the graph.
Why not? What does Science Workshop define as “Position”? How could this graph be altered
so that “Position” was redefined as “the location of the cart measured from equilibrium”?
7.
(1 pt) Using the Experiment Calculator, create a new calculation called “Position from
Equilibrium”. State the calculation formula in the table below.
Calculation Name
Position From Equilibrium
Short Name
X
Units
meters
Formula
Determine the Angular Frequency of the System:
1.
(5 pts) From your measurement, record and/or calculate the period, frequency, and angular
frequency of the resulting simple harmonic motion of the cart/spring system in the table below.
Period – T
(s)
2.
Frequency – f
(Hz)
Angular Frequency – 
(rad/s)
(5 pts) Determine the theoretical value for the natural angular frequency, , of the cart (mass) and
spring system. Explain your calculation. (See the Introduction or Section 16-3 in the text. Note:
This calculation assumes that the system is frictionless.)
(Theoretical)
Natural Angular Frequency - 
(rad/s)
Explanation of Calculation
3.
(5 pts) By what % does the experimental value of differ from the theoretical value of . Clearly
show your calculations. Is it true that the experimental value (which is slightly damped) is less
than the theoretical value (which assumes that it is not damped) as predicted?
Comparing the Graphs of Simple Harmonic Motion:
13. Questions:
 (5 pts) What is the location and direction of the cart when the velocity is at a maximum or
minimum value?

(5 pts) What is the location of the cart when the velocity is equal to zero?

(5 pts) When the acceleration of the cart is at a maximum or minimum value, what is the velocity
and location of the cart?
Activity 2: Damped Simple Harmonic Motion (20 pts)
2.
(5 pts) Copy the graphing window into the Template by using “paste special”. Paste it as if it was
a picture.
3.

Questions:
(5 pts) How does the period of the resulting simple harmonic motion change over time as damping
occurs? Support your reasoning by analyzing data from the graphs. Clearly explain your analysis.

(5 pts) How does the amplitude of the position change over time as damping occurs? (For
example: Is it constant? Is it changing linearly? Is it changing exponentially? Is it increasing? Is
it decreasing?)

(5 pts) What does the change in amplitude suggest about the total energy loss of the system over
time? (i.e. What type of dissipating forces are likely acting on the system?)
Activity 3: Forced Oscillations & Resonance (20 pts)
Important: Do not turn on the power supply until the following conditions have been satisfied:



The Voltage knob should be turned completely in the counter-clockwise position (its lowest value)
whenever the power supply is turned on and off. Note: There are two adjustment knobs. The
black one provides coarse-tuning, and the red one provides fine-tuning. Both should be turned
completely counter-clockwise.
The Current knob should be turned completely in the clockwise direction (its highest value). This
setting should not be changed throughout the entire experiment.
Check the connections between the power supply and the Oscillator/Driver to be sure that the Red
leads are attached to the + side of the power supply and the Black leads are attached to the – side
of the power supply.
5. (6 pts) At each voltage setting (and therefore frequency), first allow the system to damp itself into a
regular pattern. Then, using Science Workshop, determine the amplitude of the resulting motion and the
period of the driving force. Calculate the angular frequency of the system at each setting. Place your data
in the table below.
Voltage Setting
(volts)
1.5
2.0
2.5
3.0
3.5
4.0
7.

Period
(sec)
Angular Frequency
(rad/s)
Amplitude
(meters)
(4 pts) Copy and paste the Excel plot of Amplitude vs. Angular Frequency below.
Remember: Turn the Voltage knob completely counter-clockwise before turning the power
supply off !
11. (4 pts) Copy the graphing window of Position from Equilibrium vs. Time, Velocity vs. Time,
and Acceleration vs. Time into the Template by using “paste special”. Paste it as if it was a
picture.
12. (3 pts) Determine the period, frequency, and angular frequency of the driven system at resonance
and place the values in the table below.
Resonant Period – T
(s)
Resonant Frequency – f
(Hz)
Resonant Angular Frequency – 
(rad/s)
13. (3 pts) Compare these values with the natural period, frequency, and angular frequency of the
cart/spring system determined in Activity 1. What condition is necessary to cause a system to
resonate?