Variables:
Independent:
- Position of the ball dropping on the side of the mat (distance from that point to the middle of the bowl-amplitude)
Controlled:
- Temperature
- Air resistance
- Friction
- Mass
- Wavelength
- Circumference of the mat
Dependent:
Equipment List
Tennis ball
Time watch
Measuring tape
Pen
Paper
Ruler
Mat
Methods:
- First take the mat
- However make sure you have at least 2 people for this experiment. One person has to hold the mats together forming an arc shape for the tennis ball to role in.
- Measure the amplitude from where you are planning to drop your ball. The amplitude of the mat is the distance from the point where the ball rests to the dropping position of the ball.
- Place the ball on the bottom of the bowl to show that it’s in a stable equilibrium.
- Now carefully displace the tennis ball from the equilibrium and release it (edge of bowl)
- It will then roll back and fourth through the equilibrium.
- Start the time watch as soon as the marble ball is dropped.
- Time the tennis ball until it stops moving
- You are timing the process 4 times as it would be easier to get more accurate results.
- Now note down the time recorded.
- Do the same procedure 4 more times but then change the position from where you are dropping the ball but be sure to measure the amplitude.
Diagram set up:
Physics results
Results
Width of the mat which was bowl shaped– 66cm
Amplitude 25 cm - Time for one oscillation
Amplitude 20cm-Time for one oscillation
Amplitude 15cm-Time for one oscillation
Amplitude 10 cm-Time for one oscillation
Amplitude 5 cm-Time for one oscillation
Finding the average
For 25 cm =0.79+0.91+0.82+1:05 /4 =0.89
For 20 cm=0.86+0.93+1.0+0.89/4 = 0.92
For 15 cm= 0.92+0.99+1.01+1.01/4=0.99
For 10 cm=0.79+0.96+1.06+1.07/4=0.97
For 5 cm=0.78+1.14+0.96+0.95/4=0.95
Final data
The relation between Amplitude and time period
Horzinatal axis – Amplitude in cm
Vertical axis – Period in seconds
Discussion : I have recorded four observations for each of the positions I dropped the ball from. This is because I wanted to make my experiment more accurate thus I decided to time the movement of the ball for four times for different amplitudes. Now for my next table, which I will use for the graph, I have to calculate the average of the 4 results for each amplitude but before that I divided each time recorded by the number of oscillations it made to find the time made by the ball for one oscillation. Here in this graph we can see that the period hardly changed so it means that the amplitude affected the period very minutely. We can notice that as the points don’t have any link in between them. If we see the first 3 readings for 5,10,15 cm amplitudes, our hypothesis seems to be right as by increasing the amplitude the time period is increasing accordingly but if we notice the next 2 readings for 20,25cm amplitude, this rule does not apply .
Conclusion:
I find that the period did not increase because when we increase the amplitude it obviously means the tennis ball will be dropped from a higher position so thus it will gain more speed while falling down , therefore if the amplitude increases the speed also increases causing the tennisball to take just as long to complete a cycle as in the case of smaller amplitude. I didn’t considered the friction of air. The friction caused the tennis balls speed to slow down and led to a decrease in the length of the arc through which it passed. Like if we take an example in which drop a ball from an angle of about 60 degrees within a short number of cycles the tennis ball will not move beyond an angle of 20 degress because of the friction so it is not a continous movement. The air friction is caused when the object moving through the air and has to move air molecules aside. Also the surface parallel to the direction of the motion of the object generates friction because when the molecules of the air which collide with the surface and are thus pushed in a forward direction by the collision. Therefore, I can conclude that the period was independant of the amplitude because the periods in all five cases differ very little from eachother.
Evaluation: I felt that this experiment was accurate up to and extent however there were many things which we could have changed in our methods of doing this experiment to make it more accurate such as when we held the mat in the form of an arc shaped it was difficult to keep it the same throughout when the tennis ball was rolling so we could change this by placing the mat between a chair and the wall which would the mat into place this would make it impossible for the mat to move and the size to change even slightly so this could have cause us to get even more accurate results. Also the speed applied when I was dropping the tennis ball couldn’t be measured so we can try to be more accurate to not apply any force, so the force applied won’t affect the results. In over all in my view this experiment was properly planned, as we were able to finish it in a sufficient amount of time. To make our results accurate we tried our best by recording the time period 4 times for each of the 5 different amplitudes and then taking out the average. There were also problems when I dropped the ball in the mat it basically wobbled and moved from one side to the other and didn’t just follow the same path while moving so this might have caused some inaccuracy in the results. We could have improved this by not using a mat but something else like a bowl to roll the ball in where circumference would stay same during the whole experiment.
Follow up experiment: Since in this experiment we looked at the link between the amplitude and period, after this we can take the initiative to look and compare between two other properties. So we can look at the influence of changing the mass on the period. We can try placing different weights in a small cylindrical tube and then rolling it. The amplitude will remain the controlled variable in this case.
Bibliography
"Harmonic oscillator -." Wikipedia, the free encyclopedia. Web. 11 Jan. 2010. <http://en.wikipedia.org/wiki/Harmonic_oscillator>.
"Oscillation: Definition from Answers.com." Answers.com: Wiki Q&A combined with free online dictionary, thesaurus, and encyclopedias. Web. 11 Jan. 2010. <http://www.answers.com/topic/oscillation>.
"What is amplitude?" Indiana University. Web. 11 Jan. 2010. <http://www.indiana.edu/~emusic/acoustics/amplitude.htm>.
