Calculating error in pendulum motion

[asadpasat]

Homework Statement

I have to calculate the propagated error on g of pendulum. I pretty much measured the T of pendulum and now calculating g while increasing the number of cycles.

Homework Equations

I used the equation of propagated error and i included picture of it and my calculations.

The Attempt at a Solution

I plugged all the values into the equation but what bothers me is the size of the error. For 20 cycles I get g=9.776, but my error is 0.02. This seems like a huge error, and would mean that my g would equal to 9.78. Anyone sees any mistake?

 

[TSny]

To avoid a crick in the neck

 

[asadpasat]

To avoid a crick in the neck

Thanks! Makes it more convenient.

 

[asadpasat]

Here is picture of the equation and detail calculations.
* I don't know how to rotate the picture, sorry.

Edit: Image rotated by moderator:

 

[gneill]

* I don't know how to rotate the picture, sorry.

Most platforms have ways to rotate an image. What type of computer are you working from?

 

[TSny]

I plugged all the values into the equation but what bothers me is the size of the error. For 20 cycles I get g=9.776, but my error is 0.02. This seems like a huge error, and would mean that my g would equal to 9.78. Anyone sees any mistake?

I don't see any mistakes (but I didn't check all your calculations). Why do you think your error is "huge"?

 

[asadpasat]

Here, I figured it out.

 

[asadpasat]

I don't see any mistakes. Why do you think your error is "huge"?

Well I think it's huge because it would mean that I can trust my g only to 3 sig figs. So I pretty much throw away one sig fig.

 

[TSny]

3 sig figs seems OK to me. For 20 cycles you have a fractional error in T of about .001/1.44 ≅ .0007. But note that T is squared in the formula for g. So, the contribution of the error in T to the relative error in g should be roughly 2(.0007) ≅ .001. The contribution of the error in L to the relative error in g is roughly .0006/.51 ≅ .001. So, I don't think it's surprising that when you use your more accurate formula to determine the error in g, you find that you are only getting 3 sig. figs. for g.

 

[TSny]

Here, I figured it out.

You made an error in grinding the numbers here.

 

[asadpasat]

View attachment 112607
You made an error in grinding the numbers here.

Wow. Thanks a a lot. Now it makes way more sense for that cycle.