Complete solutions
to the equations of motion for oscillating springs or pendula require at least
a strong background in the mathematics of differential equations. Even with
this background the solution of the equations in which dissipative processes
are at work can be very difficult. In this experiment we will use a combination
of an Applet simulation and a VideoLab to investigate
damped oscillatory motion.
The basic underlying equation that we will use to model the motion of a damped spring is which can be re-arranged to give us . In this equation 'b' is referred to as the damping constant and it is a measure of energy dissipation in the system.
Part One:
"Pre-Lab"
We will spend a few minutes looking at an applet representation of damped harmonic motion and develop some strategies for determining the damping constant.
Part Two: Damped
Oscillations (VideoLab)
In this part of the experiment your
group will attempt to quantify the phenomenon of damping in the motion
of a simple spring-mass system.
VideoLab:
- each member of your group should load the following
VideoLab video clip and collect the data for a 100g mass oscillating in
a beaker of water.
- when you are satisfied that
your data looks good, save it to the PC and analyze using either LoggerPro or EXCEL
Analysis
and Things to do ....
- Try to fit your data to a displacement-time
function of the form where w and a are as we developed them in class. You can use my sample EXCEL file to assist you.
- Average the values that each of the group members got and use these averages in your report.
- From this tell me the damping constant
and k value for the spring-mass
system
that
you
used.
- Prepare a graph that shows the
decay envelope for the damped oscillation that you studied.
- Tell me about energy in the system.
What was the starting mechanical energy and how did it change over time.
What
to Hand In (by next week this time)
- a graph showing the fit between
your experimental data and the expression and the decay envelope of your damped spring-mass system.
- prepare a graph of the mechanical
energy of the system as a function of time. From this estimate the power dissipated
in the system by the damping effect of the water.
- discuss how you could design an
experiment to measure the power being dissipated by using a very sensitive
temperature probe.
- a one-page (maximum) discussion
of how well your model worked. For example, did your measured period of oscillation
agree with the theory of period for a damped spring? If not, can you suggest
some reasons (assumptions we may have made or things overlooked)?
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