Video Lab 6: Large amplitude pendulum

Video
Lab 6

The Not So Simple Pendulum

Goals

To show that a simple pendulum with small amplitude motion closely approximates simple harmonic motion
To make comparisons to the motion of the same pendulum when released with large amplitude

Prelab Preparation

In Chapter 14 (PH210) or 15 (PH220) of the textbook, review the defining characteristics of simple harmonic motion and the conditions for which a simple pendulum approximates this motion.
Review the results of our first lab (Period of the Pendulum) to find out how the period of a simple pendulum depends amplitude.
Get a head start by analyzing the first video clip (small amplitude swing).

The Video Clips

The video clips for this lab were made by PH210 students (Fall, '96). They suspended a 1-inch diameter aluminum ball from a sturdy support. They released the bob from different angles and made a number of clips. You'll be looking at two of these clips. Download the first one now.

pend0c.avi (627 kb)

Go ahead and play the clip now. You'll see that the amplitude of the swing is small, about 15°. One full cycle is shown. The markings on the meter stick at the bottom are difficult to distinguish. However, two good points for scaling are the left end of the stick and the left side of the second piece of black tape. The separation of those two points is 0.300 m.

Save the clip to your working directory and download the next one.

pend4c.avi (780 kb)

This is a much larger amplitude swing of the same pendulum as above. Again, one complete cycle is shown. The camera was moved back to allow the full span of the swing to be shown. Save this clip, too.

Analyzing the First Clip

We're not going to go into detail here about procedures. We'll just give an overview and some hints.

Mark successive positions of the bob as you've done in previous clips.
See the above recommendation about selecting scale points.
Create a fixed point at the vertex of the swing. This will come in handy later.
Move the origin of coordinates to the lowest point of the swing, and make sure the y-axis passes through the swing vertex.
Here's something you haven't done before. Create an Angle. The dialogue box for this asks for three points. Use the vertex of the swing, the lowest point (Origin 1), and the bob position (S1). This will give the angular displacement as a function of time.
Want to measure the length of the pendulum? Try this: Create a Distance. Select as your endpoints the vertex of the swing and S1. This will give you the length of the pendulum as a function of time. Of course, we hope that it's constant. (Why wouldn't it be?)

If you do all of the above, you'll end up with 5 columns. Before you paste the data into Graphical Analysis, create a 5-column data table in that program (or however many columns of data you actually have). Now here are some suggestions for things to do in Graphical Analysis. By the way, be sure to label everything clearly, use consistent units, and document your work in a text box.

Apply a sinusoidal fit to the x-t graph. Is it a good fit? Calculate the period. Compare it to the expected theoretical value for a small amplitude pendulum.
Look at the y-t graph. Why is y's period double that of x?
Now let's say you want to look at kinetic and potential energies. For the latter, you can just plot gy versus time. (Why don't you need the mass? or do you?) For kinetic energy, you need v. This isn't dx/dt or dy/dt but rather [(dx/dt)² + (dy/dt)²]^½. This method tends to propagate errors, because you have to find two derivatives and then perform several operations on them. Another way involves using the graph of angular displacement versus time. We're going to let you figure out how to use this to find KE.
Of course, once you have KE and PE versus time, you'll want to know whether total mechanical energy is conserved. How can you show this with a graph? Is the result what you expected?

That's about it for analyzing the first clip, unless you want to get fancy and find out whether the maximum angular acceleration of the bob is in agreement with the theoretical value. (You'll have to come up with the theoretical formula, but that's not difficult.)

Analyzing the Second Clip

Now you're ready to analyze the large amplitude swing. You should expect some differences from the first clip, since the motion isn't supposed to be simple harmonic. Do you expect mechanical energy to be conserved? Is the angular acceleration affected by the amplitude? We'll leave it to you to carry out a thorough investigation.

Preparing Your Lab Journal

Tape into your journal printouts of all relevant data tables and graphs. Plan your work so that these printouts fit the available space and appear in appropriate locations. Folded graphs, loose inserts, disorganized work, and unlabeled work are not acceptable.

Discussion

Provide a complete discussion in your lab journal including what you found out about the two pendulum swings and how they compare with a) theory and b) with each other. Include a discussion of error sources.

Submission

Send your Videopoint and Graphical Analysis files to the teacher via CourseInfo. Make sure that all files are named distinctively and descriptively.