Modeling a Swing with parametric functions

[nvidia69]

Homework Statement

How can one model the vertical and horizontal motion of a swing? The maximum height was 258 cm, the lowest 38cm and the horizontal movements went from 2.39m on the left to 2.44m on the right. The period was approx 2.5793 seconds.
(The data was hand collected, so it is not perfect)

Homework Equations

knowledge of sine and cosine functions

The Attempt at a Solution

So I set up a periodic equation for the x movement as x=2.415sin(2pi/2.5793 T) using the data above and then for y, y=-1.48cos(pi/2.5793 T) + 1.86. This results in a circle if the T values get large enough. So to compensate, I restricted the domain, and got a semi circle. However, there are still -T values, which makes no sense as one cannot have negative time. Is there a more accurate way to do this or any way to shift the graph to the right, to avoid negative T's?

 

[The Chaz]

...Is there a more accurate way to do this or any way to shift the graph to the right, to avoid negative T's?

Like you said, it's a periodic function so it repeats every 2.5793 seconds. The "graph" goes on forever to the right, at least in an ideal world (without air resistance, friction, etc)

 

[LCKurtz]

Homework Statement

How can one model the vertical and horizontal motion of a swing? The maximum height was 258 cm, the lowest 38cm and the horizontal movements went from 2.39m on the left to 2.44m on the right. The period was approx 2.5793 seconds.
(The data was hand collected, so it is not perfect)

Homework Equations

knowledge of sine and cosine functions

The Attempt at a Solution

So I set up a periodic equation for the x movement as x=2.415sin(2pi/2.5793 T) using the data above and then for y, y=-1.48cos(pi/2.5793 T) + 1.86. This results in a circle if the T values get large enough. So to compensate, I restricted the domain, and got a semi circle. However, there are still -T values, which makes no sense as one cannot have negative time. Is there a more accurate way to do this or any way to shift the graph to the right, to avoid negative T's?

Don't forget to notice that some of your dimensions are in meters and some in cm., so you need to use consistent units. A more serious problem is the interpretation of "period". It isn't giving you the period of your sine or cosine function. It is telling you how long it takes to swing to and fro one time. The left and right distances would be equal in a frictionless world, so you may need to use their average and assume no friction. You will need to use that value to give your T limits and to figure out the theoretical period of the cosine function.

 

[LCKurtz]

Additionally, I think you need to measure the length L of the chain supporting the swing and use

$$T =2\pi\sqrt{\frac L g}$$

for the approximate period of a pendulum swing.

[Edit] On looking at it again, I think you don't need to measure L but can use the above equation to get L knowing T. Then you have the radius of your circle arc.