AP® Physics C: Mechanics

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Difficult

Physical Pendulum: Differential Equation

APPHMC-7QIHYR

The uniform rod shown below has a length $l$, mass $m$, and pivots around point P at one end. The rotational inertia of the rod around its endpoint is $\frac { 1 }{ 3 } m{ l }^{ 2 }$.

J. Krehbiel. Created for Albert.io. Copyright 2016. All rights reserved.

Which is the correct, simplified differential equation for describing the motion of this physical pendulum for small angles of oscillation?

A

$\cfrac { {d} ^{2}\theta}{ { dt }^{ 2 } } =-mgl\sin { \theta } $

B

$\cfrac { {d} ^{2}\theta}{ { dt }^{ 2 } } =-mg\cfrac { l }{ 2 } \sin { \theta } $

C

$\cfrac { {d} ^{2}\theta}{ { dt }^{ 2 } } =-mg\cfrac { l }{ 3 } \sin { \theta }$

D

$\cfrac { {d} ^{2}\theta}{ { dt }^{ 2 } }=-6gl\theta $

E

$\cfrac { {d} ^{2}\theta}{ { dt }^{ 2 } } =-\cfrac { 3g }{ 2l } \theta $