Hogwarts Witchcraft & Wizardry Web

Pendulum Chain

Sources of error in a paper-clip chain oscillation experiment?

"Investigate the oscillations of paper clip chain and form a relation T = pn^q where T is the time period, n is the number of paper clips and p and q are constants."

If you're going to be considering a simple pendulum, there a huge number of errors you must factor in.

A simple pendulum assumes the center of mass to be at the end of the length of massless string. Your center of mass is going to be somewhere in the middle of the "string". The error in your experiment should come mainly from what you measure... so the length to the end of the chain, which could be the length of each paper clip multiplied by n paper clips (which would cause more error). Air resistance and friction (depending how you set it up) will probably be less than your measurement of length or mass. So will the error caused by taking the small-angle approximation.

You're not measuring mass because you would find, upon doing a more intensive experiment, that it has no correlation to T.

Error will also come from your time. Let's say you have an awesome stopwatch. Then your reflexes might allow you to start or stop it with 0.1 seconds of the correct time. If you let the "pendulum" swing 10 times, you'll get better error (the percentage will be 0.1/10 = 1%, let's say, instead of 0.1/1 = 10%.) But you are now at risk of lots of damping (air resistance) and things like that.

So the summary is:
in measuring period, your error comes mainly from
> measuring time
> measuring length

Look up "error propagation" to figure out what your total error in period is. (It's the square root of the sum of the error percentages squared).

Pendulum Chain finishing

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