Now i could go ahead and see whether this is close to the accepted value, and i could do that. That would be a little strange, so i will go ahead and work that out 2 significant figures and we get g is equal to 9.87 meters per second squared i'll call it 9.9 meters per second squared. And so that gives us g equals pi squared okay, now we know it's not exactly equal to pi squared. Maybe call that 4.0 second square and what we know is that that should be equal to 4 pi squared over g and so g is basically for pi squared over 4.0 meters per second squared and notice that that very nicely makes the 4 cancel. I have a fairly nice straight line and in fact my slope is basically 4 seconds squared per 1 meter to the precision i've got there. Okay, so we'll go ahead and just try to draw the straight line through there and i do see. This is kind of tedious but necessary, 1.04. Let'S see, let me just try to draw that by hand since yeah, i may not be able to um, actually draw it through there like i set drawing tools. But let's try to draw a straight line that goes through the origin and tries to go through all those pointsit might be a little bit easier to draw it off to the side than move it up there yeah the drawing tools, aren't the best, but we'll try To move the graph, which i think i did, i may not be able to move that. I will try to draw a line in a straight line, not usually very good at that. You can see it's a very nice pattern, 3.2 and then 4. It may not give us very precise results, but it will be easy to plot and work with okay, so we'll go ahead and make some fairly big points i'll make them triangles here.8. Don'T i we should be a good with 1, so here is l in meters and period squared and second squared and notice that if you come back on to figs, it's a little bit easier to plot. Make this look a little easier to work with 0. In fact, we're probably good with just 2 significant figures, so we will go ahead and make a plot and then we'll go see what the slope gives us and i'll go ahead and start at 0. So let's go ahead and figure the period squared, and i am going to leave this to the same number of significant figures that occur in the period, because you can't generate more significant figures than what you start with. I won't be too surprised if this does not come out to give us a good value of g could be on the moon, so. So here's some dataassuming that we are on earth, but we may not be so. So, let's take a look at some experimental data length in terms of meters and period squared in terms of seconds and actually it's a little bit safer to measure, say 10 periods here it will just show the period and seconds but measure a whole bunch of periods, Because then, your reaction time won't come into play and then we'll go ahead and take the periods squared. So if we plot t squared versus l notice what we should get as the slope of the function, the slope should be 4 pi squared over g and the y intercept should be 0. Then, if we plot t squared that should give us 4 pi squared times, l over g. In any event, let's see if we measure the period as a function of length in so here's the experiment change the length of the pendulum and measure its period. Most things with gravity, the mass does cancel out of the dynamics. Constant and g takes the place of the mass so notice that this is mass independentlike. So this looks very similar to the simple harmonic oscillator period, but l takes the place of the spring. We won't prove that, but it is kind of fun to work that out and the period of the motion in time is given by 2 pi times the square root of l over g. It is something to be aware of if you are making measurements so from point of support of the string to the center of mass of the bob, just in case that bob has some extent to it and it turns out that the period so the for small Displacements call that small theta theta executes simple harmonic motion. Typically, there is a very small but heavy pendulum bob that has negligible length, but i should point out that that length really should go from the point of support to the center of mass of the bob. So simple pendulum is simply a string tied to a point of support on a ceiling. Here i'll start with a few general remarks about a simple pendulum and we'll use, but we know about the simple pendulum uh in order to look at some experimental data where we can find the acceleration of gravity or the strength of earth's gravity um.
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