A uniform stick of length L = 1.3 m , width W = 13.9 cm , and mass M = 3.7 kg os

Question

A uniform stick of length L = 1.3 m, width W = 13.9 cm, and mass M = 3.7 kg oscillates as a physical pendulum and pivots about point O as shown in the Figure.
A--What is the period of the pendulum if x, the distance from the pivot point to the center of gravity of the pendulum, is equal to 0.26 m?
B--Determine the distance x for which the period of the pendulum has a minimum value.
C--Calculate the minimum value of the period of the pendulum.
Note: Letter A is 1.80 seconds, Letter B is 0.377 meters.
NOTE: Letter C is not (0.235 s,1.86s, 0.0176s, 2.29s, 1.622s)

Explanation / Answer

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For part B.

We have T = 2? sqt(I/mgh)

Hence for Maximim h , T will be minimum

hmax = L/2= 1.3/2 =0.65 m

For part C

T = 2?sqt[ (1/3 mL^2)/mg(1/2 L)]

= 2?sqt ( 2L/3g)

=1.86 sec

Hope you will understand the solution.

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