Math 294-0138
D. Prapavessi, Fall 2009
The Springs Project
You must work in your assigned groups of four for this project. Each group must work with the same spring throughout, and turn in one paper. The deadline to submit your work is Monday, 10/5.
1.
Determine the spring’s constant k in N/m By Hooke’s law
;
stretch the spring by attaching various weights and get at least 5 measurements
of the displacement.
Remember that g = 9.80 m/sec2 in your calculations.
2.
Attach a mass m on the spring and generate an initial value problem
for the spring motion with initial conditions
.
Mark a position along the path of the spring, and record the first 5 times the
spring passes through the given point. (You probably want to repeat this
experiment 3 - 4 times to make sure your data is reliable). Record the time at
which the motion stops.
3. a) What is the frequency of the motion?
b) What is the pseudo period of the motion?
c) Estimate the damping constant c.
4.
Find the position function
of
the mass at time t. On the same graph, plot together the function
and
the recorded data from part 2.
5. As shown in the figure below, attach the glider to the spring. Simulate an initial value problem by displacing the glider to the right, a given stretch. Release the glider and setup a photogate to measure the velocity of the glider at different positions along its track motion. Measure the velocity at 5 different locations, 5 times for each location
6.
Use Euler’s method to calculate an approximation to the position
function of the glider at
time t, and graph it- does it appear that
is a case of spring damped motion ?
Note: a) When you take your measurements, please remember to measure the equilibrium length of the spring when it is horizontal. b) Please keep your units consistent in the SI system so that mass is measured in kg, work is measured in joules (J) etc.
In about 30-50 words, please evaluate yourself, your partner and this project. Each student must complete his/her own online evaluation accessible from our course website http://voyager2.dvc.edu/faculty/dprapavessi/Fall2009/courseinfo0138.htm