## MOVIESPlease note: If the movie is too small,please watch via youtube using the YOUTUBE button on bottom right of each video. And, some videos have much higher quality. Find the HD version using the gear icon. Pendulum: Display, X-Intercept The lab manual asks you to mis-measure the length in order to show how systematic offsets may appear on a plot. Find the HD version using the gear icon. |

I am wondering about the intercept for the graph of T^2 vs. L. I don't know how I can account for the intercept as being the initial period. I'm a little bit confused. Does the intercept account for the fact that there is still a period when the length cannot be accounted for? Can you please help me? | Anonymous Thu. 13, Nov 2003, 16:14 |

Think of the x-intercept when you have a positive y-intercept. (Sketch a graph and continue the trendline until it hits the negative x-axis when y=0.) Does this lead you to believe there may be a length measurement offset? | Douglas Fri. 14, Nov 2003, 14:59 |

Hi Douglas, Confused about question 4 on the post-lab, I read the above post and haven't made sense of it. I guessed that the significance of the vertical (y-axis) intercept was simply experimental error, since it seemed strange to have a negative period, not to mention a negative square of a period (as was the case with my data). You mention comparing the situation to the case of a positive y-intercept, which also is strange because it would indicate that a period is possible under the condition of negative length. I think I missed the point - what do you mean by "length measurement offset"? And what does the former student mean by "initial period"? | Wilson, Alexander Tue. 30, Mar 2004, 15:31 ac1wilso@ouray.cudenver.edu |

Hello, Alexander. I agree, your negative intercept is strange in the sense that it yeilds an imaginary Period!But consider this: the data hits the horizontal axis (Length) at some positive value before it hits the T^{2} axis. That positive value on the Length axis might be a systematic length offset.Imagine this: Measure each Length for the experiment by measuring (incorrectly) to the end of the pendulum bob. The center of gravity for the pendulum bob is 0.007[m] from the end of the bob. You should have only measured to the center of gravity. You plot your data. You get a negative T ^{2} intercept; but your data hits the Length axis at +0.007[m]. That's because all the data was shifted to the right by 7[mm] since you incorrectly measured the c.g. of the pendulum bob.Other students reading this might want to try this when they do the experiment. Purposefully measure the length incorretly; but be consistently wrong!!! Alexander, you can adjust your data table by adding 0.005[m] to all your lengths and see if it shifts the data to the right. What would happen if a student measured to the top of the mass bob instead of the c.g.?????? | Douglas Wed. 31, Mar 2004, 05:30 |

Question #5 on the post lab: "Further this experiment by stating a reasonable, new question with answering procedure." Can you either restate this or provide some clarification as to what your looking for. I'm a bit confused about this question. Thanks | Anonymous Thu. 28, Oct 2004, 09:38 |

You did the pendulum experiment. If you were to come to class next week and do the experiment again, what could you change and what new question would it answer? This is supposed to be the end of the scientific method: After finishing an experiment, ask a new question, come up with a hypothesis, and do the experiment over again but this time with the changes that will hopefully confirm or contradict your hypothesis. So, what new question can you ask, and what procedural changes are required to re-perform the experiment again and get the answer to your new question? Thanks for asking. Please let me know if you need further clarification, :)oug | Douglas Thu. 28, Oct 2004, 10:08 |

Hi Douglas: Would you please clarify a little bit more question # 4. I just don't understand how are we suppose to calculate the lenght offset from the "vertical intercept"? By the way do you mean the y-intercept? Thank you, I apprecaite your help. | Galindo, Cesar Mon. 23, Apr 2007, 14:07 cdgalind@ouray.cudenver.edu |

The y-intercept is the T^{2} "offset."The x-intercept is the Length offset. y = mx + b b is the y-intercept. But we want to know the x-intercept. Set y = 0 and find x. x = -b/m (for y = 0.) I hope this helps a little. | Douglas Mon. 23, Apr 2007, 16:11 |

There is a PostLab question about a length offset. What does that mean? | Anonymous Thu. 15, Nov 2007, 08:35 |

There is a question on the PostLab about the Length offset. What does the "Length Offset" mean? Better yet, what does the vertical intercept mean? If the vertical intercept is positive, it means all the data was measured that much time too much, systematically (regularly...) But if the intercept is negative, then the stopwatch is consistently too slow by that amount. We would not expect a "human" to be so perfectly consistent in being off in time a set amount for each run. So, we must then draw our attention to the x-intercept instead of the y-intercept. The x-intercept would be the length-offset. Now that sounds more reasonable. I can imagine someone consistently measuring too long (say, to the end of the bob instead of the center of the mass bob.) Or maybe someone measured to the knot above the mass bob, thus a consistent length measurement that is too short. The too-long length offset would yield a negative vertical intercept. The too-short length offset would yield a positive intercept. Given the equation for the plot, how can one determine the x-intercept in order to equate that to the length offset? | Douglas Thu. 15, Nov 2007, 14:37 |

Hello, Douglas Can you, please, help me with the question 2. What would uncertainty of Length be? Is it Length offset? If we did measured to the center of the mass bob - is it the precision of our measuring tool then? thank you | Anonymous Fri. 24, Oct 2008, 16:19 |

Yes, the precision of the tool is the answer. σ _{length} is the measurement uncertainty in the length of the pendulum. It can be regarded as the resolution of the metric scale you are using to measure the length.The length offset is something different. Length offset refers back to that in the measurement which was systematically shifted from the expected 0m length for 0s ^{2} Period^{2}.σ _{length} on the other hand refers to uncertainty in the measurement which is regarded not as systematic error but random error. | Douglas Sun. 26, Oct 2008, 04:41 |

What can be done to lengthen the period of a pendulum? Also if so many pendulum cycles are given and a duration of time is given for the cycles of a pendulum, is there a way to figure the period? | Martin, Brandon Thu. 06, Nov 2008, 18:44 bmart111@msudenver.edu |

Period is defined as the time it takes for one complete cycle (back and forth swing) for a pendulum. If you know the total time for say 12 cycles, then the Period is Total Time / 12 cycles which would give you the time for one cycle, or the Period. T = 2π (L/g) ^{1/2}Where T is period of pendlum; L is length of pendulum; and g is the acceleration due to gravity. T = 2π (L/g) ^{1/2}If L is increased, then T will increase. If g is decreased, then T will increase. | Douglas Fri. 07, Nov 2008, 08:06 |

I worked out the equation you has said to use for question 4, the one about the lenght offset, and i got the wrong answer. My question is this, is the lenght offset suppoed to be a negitive number becasue it falls on the negitive x-axis or is it supposed to be positive becasue we are measuring the distnace from the origin? | Martin, Brandon Thu. 13, Nov 2008, 16:17 bmart111@msudenver.edu |

If the x-intercept is negative, then the length offset is negative. In this case, the string was measured systematically too short. | Douglas Fri. 14, Nov 2008, 05:15 |

In prelab question #5 we are given a stopwatch reading of 1:3.30, I have no clue how to read this, is it a ratio? If this is a time it is baffling me. | Radulovich, Michael Tue. 20, Apr 2010, 13:38 radulovm@msudenver.edu |

Standard Stopwatches read as such HH:MM:SS.ss Hours:Minutes:Seconds.Decimal Seconds. 1:3.30 is 01:03.30 1 minute, 3 seconds, 30 hundredths of a second. or 63.30 seconds. | Douglas Tue. 20, Apr 2010, 14:49 |

Post lab question 3 asks for the theoretical equation. Do you mean the equation for our theory plot on the graph? Because we weren't asked to find the equation of that line. | Anonymous Sun. 25, Jul 2010, 15:31 |

The question states: State the plot equation for your data as well as the theoretical equation. These two equations should appear on your plot. One describes the data you took; the other describes the theory line that was prescribed for the plot. The equation for the theory line is known for three reasons: (a) physical values and their units for each axis are known; (b) the intercept for the theory line is zero; (c) and the slope is the theoretical slope found by evaluating 4π ^{2} g^{-1}. | Douglas Sun. 25, Jul 2010, 17:28 |

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