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 New Users New to PHF? Post up here and introduce yourself! May 28th 2019, 02:03 AM #1 Junior Member   Join Date: May 2019 Posts: 2 Compound pendulum a compound pendulum is formed by suspending a heavy ring from a point on its circumference . determine the time period of oscillation of radius of the ring is 1m. Time period T =2π √I/mgl I took I= mR^2/2 and l=r which gave me an answer of 1.41s . But the actual answer is 1.28s what am I doing wrong?   May 28th 2019, 11:03 AM   #2
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 Originally Posted by McKenziemc799 a compound pendulum is formed by suspending a heavy ring from a point on its circumference . determine the time period of oscillation of radius of the ring is 1m. Time period T =2π √I/mgl I took I= mR^2/2 and l=r which gave me an answer of 1.41s . But the actual answer is 1.28s what am I doing wrong?
From your verbal description, I gather the compound pendulum looks something like the attached figure. Would that be correct, or no?   May 28th 2019, 11:16 AM #3 Junior Member   Join Date: May 2019 Posts: 2 Yes.   May 28th 2019, 02:08 PM   #4
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 Originally Posted by McKenziemc799 Yes.
Unless I'm missing some other information, I disagree with both your calculation for period and the "actual answer" value.

Using the parallel axis theorem,

$I = I_{com} + md^2$

for a uniform ring of mass $m$, $I_{com} = mr^2$ and $d = r$

so, $I = mr^2 + mr^2 = 2mr^2$

$T = 2\pi \sqrt{\dfrac{I}{mgd}} = 2\pi \sqrt{\dfrac{2mr^2}{mgr}} = 2\pi \sqrt{\dfrac{2r}{g}}$

For $r= 1 \text{ m } \implies T = 2\pi \sqrt{\dfrac{2}{g}} \approx 2.84 \text{ sec}$  Tags compound, pendulum, time period Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Physics Forum Discussions Thread Thread Starter Forum Replies Last Post jackthehat Kinematics and Dynamics 5 Sep 6th 2017 12:02 PM jackthehat Kinematics and Dynamics 4 Apr 6th 2017 10:47 AM ambitious Periodic and Circular Motion 4 Apr 12th 2016 01:34 PM Nusc Advanced Mechanics 0 Mar 3rd 2010 03:47 PM Aladdin Kinematics and Dynamics 1 Jan 10th 2010 08:18 PM 