Purpose
1) Develop the sinusoidal equations of motion for a pendulum.
2) Compare the experimental period to the calculated period T=2π√(L/g)
2) Compare the experimental period to the calculated period T=2π√(L/g)
Materials
Ring Stand
String
Mass
Measuring Board
Flipvideo Camera
LoggerPro Software
String
Mass
Measuring Board
Flipvideo Camera
LoggerPro Software
Procedure
We begin by tying a string through two points on a ring stand and hanging a mass on the string. We must tie it in two places in order to maintain simple harmonic motion. Were the string more free to pivot freely, we would encounter complex harmonic motion.
After setting the measuring board behind the newly created system, we pull the mass back to a distance of 11cm and release. The video captures the motion.
Moving the video to Window's Movie Maker, we are able to move frame by frame through the video and plot the path of the mass along the axis of motion.
Putting this data into LoggerPro, we are able to perform a sinusoidal regression.
We may then use the length of our string to test the theoretical period against the actual period.
After setting the measuring board behind the newly created system, we pull the mass back to a distance of 11cm and release. The video captures the motion.
Moving the video to Window's Movie Maker, we are able to move frame by frame through the video and plot the path of the mass along the axis of motion.
Putting this data into LoggerPro, we are able to perform a sinusoidal regression.
We may then use the length of our string to test the theoretical period against the actual period.
Data
L = 46cm = 0.46m
Data Analysis
Since L = 0.46m we are able to determine the theoretical period of our system using the equation
T=2π√(L/g) = 1.36 s
The period we achieved in our experiment was 1.33 s
The percent error is (observed - expected) / (expected)
(1.33 - 1.36) - 0.022 = 2.2% error
1.36
T=2π√(L/g) = 1.36 s
The period we achieved in our experiment was 1.33 s
The percent error is (observed - expected) / (expected)
(1.33 - 1.36) - 0.022 = 2.2% error
1.36
Conclusion
Our data yielded the sinusoidal equations:
X(t)
V(t)
A(t)
It uses +cos because the mass was released from the positive extreme at t=0.
Our period of 1.33s was within 2.2% error of the expected value of 1.36. Something that may have accounted for our number being lower is a slight rounding error in measuring the string.
It was stated in the procedure that the string was tied to the ring stand at two different points. We must tie the string in two places in order to maintain simple harmonic motion. Were the string more free to pivot freely, we would encounter complex harmonic
motion.
X(t)
V(t)
A(t)
It uses +cos because the mass was released from the positive extreme at t=0.
Our period of 1.33s was within 2.2% error of the expected value of 1.36. Something that may have accounted for our number being lower is a slight rounding error in measuring the string.
It was stated in the procedure that the string was tied to the ring stand at two different points. We must tie the string in two places in order to maintain simple harmonic motion. Were the string more free to pivot freely, we would encounter complex harmonic
motion.