# Videos of Simple Harmonic Motion

## Table of contents

Professor Harlow has recorded 8 videos of Simple Harmonic Motion which you can download to your computer and read into the Tracker Software.

Videos 1 - 4 are of a hanging mass on a spring:

Video |
Mass [kg] |
Spring Constant [N/m] |

Video 1 | 0.100 | 6.6 |

Video 2 | 0.100 | 6.6 |

Video 3 | 0.100 | 3.3 |

Video 4 | 0.100 | 3.3 |

Videos 5 - 6 are of a pendulum, which is a mass suspended from a pivot, free to swing back and forth. Length is the distance from the center of the mass to the pivot.

Video |
Length [m] |

Video 5 | 0.33 |

Video 6 | 0.33 |

Video 7 | 0.33 |

Video 8 | 0.19 |

Your pod should analyze at least two videos from the above. Suggested pairs of videos that are interesting to compare are: Videos 1 and 2. Videos 2 and 4. Videos 5 and 6. Videos 6 and 8.

**For each video, please compare the following 3 tasks**:

### Task 1.

Produce a plot of position versus time for at least one or two complete oscillations. Be sure to calibrate your distance scale, and choose a coordinate system so that the motion is centered on the origin. Include a screenshot of the motion in your slides, and include the graph of position versus time you produce.

### Task 2.

Do a fit to the position versus time graph. This is accomplished by double-clicking on the graph. Choose "Sinusoid" as your fit function. If you click the checkmark beside "Autofit" it will try to fit the parameters A, \(\omega\), and \(\phi_0\) for you. However, the Autofit sometimes does not work if it doesn't have a good "initial guess". If your fit looks really terrible, first unclick the checkmark, then manually type values of A, B and C into the fit parameter boxes until you get a curve that is pretty close. Then click the Autofit again and this time it should find the fit. Include the graph of your best fit in your slides, and discuss what you got for A, \(\omega\), and \(\phi_0\) . Discuss the units and estimate uncertainties for these quantities.

### Task 3.

From your fit of position versus time, you should have values of A and \(\omega\). The maximum acceleration of the motion in this direction should be approximately \(A \omega^2\). Compute what this should be, and look at a plot of acceleration in the direction of interest versus time. Does your predicted maximum acceleration match what you measured?

**Lastly, once you have completed the above three tasks for 2 different videos, there is one more task:**

### Task 4.

Compare A and \(\omega\) for the two videos you analyzed. Are they the same or different to within uncertainties? Do you expect them to be the same or different? Discuss the reasons for the values you measure.