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Time period questions

Here is the question:

Gently displace the mass and release it so that it performs vertical oscillations. Make measurements to determine the period T of the oscillations.

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So here is what I did:
Time for 20 oscillations = t1 (2 d.p)
Time for another 20 oscillations = t2 (2 d.p)

Average time for 20 oscillations = (t1 + t2)/2 (2 d.p)

Time for one oscillation, T = { (t1 + t2)/2 } / 20 ---> this is your answer correct to 1 decimal place.

Right. Next question:

Estimate the number of oscillations that would need to be timed in order to make the percentage uncertainty in T equal to 1%. Show your working.

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Let error in one reading be x

So we use the formula:

2x/T = 0.01
where T = { (t1 + t2)/2 } / N (N is the number of oscillations).

We use the above formula to find out N.

Here are my concerns:
Is the working above correct for the two questions?
What on Earth is the error in timers? (for protractors it is 1deg; for rulers it is 1mm).

Thanks friends.
I am getting that heartpounding, gutwrenching, vomit inducing exam jitters right about now. Exam is only a few days away.

Reply 1

teachercol

The error in a hand held stopwatch is about 0.1s so you need to time for at least 10s.

Reply 2

batboy

0.1s. Sweet.

One of my mark schemes (not the mark scheme for this question) states:
If repeated readings have been done, then the uncertainty must be half the
range.

Then for another question, the mark scheme says:
Accept ∆t = 0.1 s to 0.4 s.

In the above two questions, what is the best practice? The difference of t2 and t1 divided by 2? Or use 0.1s as the error period?

Once we have established the error, is the working for the second part correct?

Sorry for being a little picky about the details so much. I know that I have to attain every little mark I can in order to get that elusive A grade!

Reply 3

teachercol

Well - either method is acceptable. Generally go with the one that gives greater error.

I find it easier to work out the time you need to time for to keep error to 1% then work out how many oscillations you need.