Physics Help Forum Simple pendulum problems

 Dec 1st 2012, 09:37 PM #1 Junior Member   Join Date: Dec 2012 Posts: 1 Simple pendulum problems 1. Why both L of left hand and right hand figures are different? 2. Why mg is put on the right end, not middle of the bar, in the right hand figure? Attached Thumbnails
 Dec 3rd 2012, 08:38 AM #2 Physics Team     Join Date: Jun 2010 Location: Morristown, NJ USA Posts: 2,354 1) The left hand figure is a traditional pendulum, and the period is dependent on the length of the pendulum. The right hand figure uses the quanity 'L' to help define the value of the spring constant - the assumption being that under weight mg the beam deflects distance L. The period of a typical spring-mass systems is 2 pi sqrt(m/k), but in this case you have a rotating beam and taking into account the rotational inertia and torques being applied the period turns out to be 2 pi sqrt(m/4k). Replace k by 4mg/L and you get the equation provided in the figure. 2) Because it works top make both fomulas the same. If the weight mg was placed at the same point as the mass teh equation woulw end up being T= 2 pi sqrt(L/(2g)).

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