Lab - Oscillation Simulation
Day 1 - Part 1: Setting up the Simulation. 10
minutes.
In this part of the lab we will set up all the
parameters needed to model the oscillatory motion of a mass on a
spring. There are five total variables we will define and reference
in our simulation. By defining these separately from our algorithm,
we make it easy to adjust for different settings. The first
variable is the “time step”, which is basically the resolution of
our simulation, and is defined for you.
Two of these variables are physical parameters of the
mass-spring system. The last two are called the “initial
conditions” of the system, that define the state of the system at
time 0.
We will need:
“Time step”
Spring constant
Mass on the end of the spring
Initial position
Initial velocity
Choose reasonable values for the initial conditions and
physical parameters you defined above. For the “time step”, we will
use 0.1 s. Fill these values in on the spreadsheet in columns H-K.
Row 1 is the header (remember to include units!), Row 2 is the
value. Column L is filled in as an example.
Use the equations on the class slides to help you fill
in the columns for time, position, velocity, and acceleration. Drag
these columns down to simulate a longer amount of
time.
Day 1 - Part 2: Graphing the Motion. 6 points. 30
minutes.
Insert three graphs, one each for position, velocity and
acceleration. Simulate enough motion to include between three and
five full periods of motion. You can drag your columns down farther
to increase the time, or you can change your physical parameters to
change the period!
(0.5 points) In column M, calculate the period of the
oscillator. It should match what you see on your graphs! Recall
that the Period of a pendulum can be calculated using:
(1.5 points) Copy your position graph here. Be sure to
label the axis and title!
(1.5 points) Copy your velocity graph here. Be sure to
label the axis and title!
(1.5 points) Copy your acceleration graph here. Be sure
to label the axis and title!
(1 point) Describe how the amplitude of the graph
behaves over time. Does this make sense? Why or why
not?
Day 1 - Part 3: Energy in the System. 3 points. 5
minutes
Fill in the columns E-G on the spreadsheet for: Elastic
Potential Energy, Kinetic Energy, and Total Energy. You should know
how to calculate these!
Create one chart that has all three values on it
(Elastic Potential Energy, Kinetic Energy, and Total
Energy).
(1 point) Copy your comprehensive Energy graph here. Be
sure to label the axis and title!
(1 point) Describe how the Total Energy behaves over
time. Does this make sense? Why or why not?
(1 point) What might be the cause of this
observation?
Day 2 - Part 1: Calculus Solution. 6 points. 30
minutes
Today we will fix the issues we saw yesterday. Using the
power of calculus, we know that the motion of an oscillating system
can be described using the following equations.
Where
First, we need to redefine our simulation parameters in
columns H-J. This time we need:
“Time step”
(1.5 points) Add reasonable values for , , and to Row 2 of Columns
H-J.
(0.5 points) Calculate the value of in column
L.
Now, use the equations above to fill in columns B-D,
simulating the motion of the mass-spring system for three to five
full periods.
Create three graphs, one each for position, velocity,
and acceleration.
(1 point) Copy your position graph here. Be sure
to label the axis and title!
(1 point) Copy your velocity graph here. Be sure
to label the axis and title!
(1 point) Copy your acceleration graph here. Be
sure to label the axis and title!
(1 point) Describe how the amplitude of the graph
behaves over time. Does this make sense? Why or why
not?
Day 2 - Part 2: Energy. 2 points 20
minutes.
Finally, let’s check the energy values.
Calculate the Elastic Potential Energy, Kinetic Energy,
and Total Energy in the system using columns E, F, and
G.
Again, plot all three types of energy on a single
graph.
(1 point) Copy your comprehensive Energy graph here. Be
sure to label the axis and title!
(1 point) Describe how the Total Energy behaves over
time. Does this make sense? Why or why not?
Excel/Google Sheets:
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