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# Answer to Question #3218 in Mechanics | Relativity for ZherVin

Question #3218
A uniform stick of mass M and length L is pivoted at one end. a.)Find the period of oscillation for small angular displacement. b.) Find the period of oscillation if the stick is pivoted about point P a distance x from the center of mass.
1
Expert's answer
2011-06-23T17:09:25-0400

T = 2&pi;/&omega; = 2&pi;&radic;(I/gML),
where I is the moment of inertia of a uniform stick of mass M and length L is pivoted at one end.
I=(ML2)/3.
So
T = 2&pi;/&omega; = 2&pi;&radic;(I/gML) = 2&pi;&radic;(((ML2)/3)/gML) = 2&pi;&radic;(L/3g).
The period of oscillation if the stick is pivoted about point P a distance x from the center of mass

I=(ML2)/12+Mx2.

And we have
T = 2&pi;/&omega; = 2&pi;&radic;(I/gML) = 2&pi;&radic;(((ML2)/12 + Mx2)/gML) = 2&pi;&radic;((L2/12+x2)/gL).

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