3. Your spreadsheet should be saved or exported in either .xls (Excel)
or .odf (Open office) format. I use Open Office, but either format
will be fine.
4. You are to work on this assignment by yourself. No outside help is
allowed. If you don’t know anything about spreadsheet programming,
this would still be a good assignment for you to try, but you must
do it on your own.
5. Any departure from steps 1 – 4 results in the award of zero points.
Now the specifics. You are to create a spreadsheet that compares the displacement, velocity and acceleration of a bouncing ball, vs time, and the same quantities of a vertical mass on a spring over one full cycle. Though these are both examples of periodic motion that seem outwardly similar, they are in fact quite different. In one case the /dominant/ force that motivates the system is described by Hooke’s Law, in the other it is gravity. Both systems are completely conservative.
You may use any /period/ for one full cycle that you wish, but, you must divide whatever period that you use into 100 intervals. If, for instance, you decide on a period of 10 seconds, you’d have intervals of 0.1 seconds, which would generate 100 data points. Whatever period that you decide is fine. Just make sure to generate 100 data points.
The amplitude of the mass-spring does not have to be the same as the height of the ball bounce, but the period does.
For both systems you will create a minimum of 4 columns to be labelled:*displacement, velocity, acceleration, time* (anything else you need you may create as well). You will use the appropriate kinematics, either linear or harmonic, to determine each of these kinematic values at 100 intervals over one full cycle. Your spreadsheet is to perform the calculations and display the values. Round appropriately.
Note that the functions for the mass-spring system are continuous, and actually easy to calculate once you get the kinematic formulas programmed properly (remember to use radians!).
For the bouncing ball, assuming that it starts it’s cycle at the beginning of it’s descent at /t/ = 0, there will be a discontinuity in the displacement, velocity and acceleration functions as the ball hits the ground, halfway through the cycle. You may ignore the brief force supplied by the ground on ball as it bounces, and therefore ignore the discontinuity in the acceleration function, but you will have to come up with a test to flip the signs of values necessary to compute the displacement and velocity values as the ball reverses direction and moves back up to it’s starting point. A simple test involving any time of flight value greater than that required to reach the ground from rest should suffice. When the ball bounces back to it’s original height, the cycle is complete.
Once you have computed 100 data points for each system, you are to create plots for displacement vs time, velocity vs time and acceleration vs time for each system. 100 data points should produce nice curves all by themselves, but should you go the extra step and try some data-fitting, I will consider that a bonus. Do not embed these in the main sheet. Instead, create separate sheets that I can access through the tabs at the bottom of the main sheet page. There should be six of these.
These will not be evaluated by the grading staff, they will be evaluated by me. I will award points based on originality, elegance, efficient programming, appearance, fidelity to instructions and wow factor. I have no pre-conceived maximum value in mind. Please note that effort is not among the criteria that I have listed. If you want points on this, you must do a respectable job. I will be checking your spreadsheet cells to look at your calculations, so don’t lock them.