# Amplitude and pendulums

when does amplitude start affecting the period of the pendulum?

I know large amplitudes do.. and I've tried looking it up but none of the equations out there make sense.. :S

## Answers and Replies

The equations for a pendulum are idealized, meaning that a pendulum does not exactly follow simple harmonic motion. The idealization is this: somewhere in the equations, sin(theta) is simply referred to as theta, which is relatively valid for small angles of theta (the difference between sin(x) and x for small x is negligible...the difference becomes noticeable for larger values of x, which is why the SHM equations for the pendulum bring in more discrepant values for larger angles).

The equations for a pendulum are idealized, meaning that a pendulum does not exactly follow simple harmonic motion. The idealization is this: somewhere in the equations, sin(theta) is simply referred to as theta, which can be taken to be true for small angles of theta (the difference between sin(x) and x for small x is negligible...the difference becomes noticeable for larger values of x, which is why the SHM equations for the pendulum bring in more discrepant values for larger angles).

We havn't learnt ANYTHING about simple harmonic motion yet :S
.. how large do these angles have to be until we notice the "descrepant values"
and what equations are you refering to :S

oh...so you haven't learned much on SHM yet...
well...to give you an example of how large the angles have to be, go ahead and do this:
Find the difference between sin(x) and x for: x=.01, .1, .2, 1.0, and 2.0. You'll notice that as the values grow larger, the difference becomes larger (more noticeable). The larger the difference, the more effect the amplitude will have on the period of the pendulum; the smaller the difference, the less effect it has. So, technically the amplitude affects the period at all angles...the effect becomes more noticeable as the angles grow larger.

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I risk sounding stupid

what is sin(x) and what does it represent?1