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| 2002/8/2 [Science/GlobalWarming] UID:25477 Activity:high |
8/1 If I want a pendulum of period 1 sec, what is the length I should
have? I know the gravity and that the pendulum is independent of
its weight. Thanks!
\- hello, making some simplifying assumptions, like the moment
of intertia is about that of a point mass at length l from the
fulcrum, and angle between the pendulum arm and the vector from
the funcrum to the center of mass isnt too large then
T = 2pi sqrt(l/g). Do you need a pendulum with large amplitude?
Also I assume this is in simple pendulum like a grandfather clock.
If you have a more complicated object thenthe radius of gyration
is k = sqrt [moment of intertia(w.r.t. center of mass)/mass] ...
I assume you know what a moment of inertia is.
[mnemonic: pi^2 is actually pretty close to the grav acceleration
at the earth surface ... this is useful if you have to do approx
on the back of an envelope. so figure a quarter meter. this isnt a
homewortk problemis it?]
\_ of course it was a homework problem --!OP
\_ isn't it easier to just find the
integration [intergation of (cos Angle)*gravity]*distance ?
\- the newtonian approach with some simplifications is not
too difficult. a richer approach is the "Highbrow
mechanics" which has at it's core the kinetic and potential
energy functions rather than the newtonian s''=v'=a func
appriach. however you may need a little geometry and some
knowledge of elliptical integrals. ok tnx.
\_ I found some notes from an old math class with elliptical
integrals on it. I used to know that stuff. I feel
really dumb now.
\_ More like your brain has pushed that crap aside for
more important things. |
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