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11/23 |
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. |
11/23 |
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