Absolute error due to reaction time when timing with a stopwatch

[Ryker]

Homework Statement

We are given that the reaction time for pressing the stopwatch is 0.2 s (we are measuring 15 swings, t₁₅ = 30.45 s) and we need to determine the absolute error in one swing.

The Attempt at a Solution

My question here is whether the absolute error for those swings is then 2 x 0.2 s = 0.4 s or is it still only 0.2 s, because the reaction times "cancel out", ie. since you're going to be within 0.2 s of proper time on your first press of the button, even if you do press 0.2 s late for the second press, you're still within 0.2 of proper time. I'm really puzzled here as to whether you need to add those or not. On one hand, I can see why you wouldn't, but then on the other hand, perhaps the reaction time error also takes into account the fact that you might press the button early.

Oh, and I also take it that t₁₅ is irrelevant here, because

\delta t_{1} = \frac{1}{15}\delta t_{15}

Is this correct, by the way?

Anyway, thanks in advance.

 

[verty]

I think the stopwatch is only pressed after 15 swings, so it is pressed 0.2 second after the 15th swing completes.

So if you calculate the time for one swing, it is off by how much?

(This is how I understand the question.)

 

[Ryker]

I think the stopwatch is only pressed after 15 swings, so it is pressed 0.2 second after the 15th swing completes.

So if you calculate the time for one swing, it is off by how much?

(This is how I understand the question.)

Alright, thanks, it turns out it was meant so that 0.2 s was the total error, and you just had to divide that by 15 to get the desired absolute error for the period T.