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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.
Expert's answer
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T = 2π/ω = 2π√(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 = 2π/ω = 2π√(I/gML) = 2π√(((ML2)/3)/gML) = 2π√(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 = 2π/ω = 2π√(I/gML) = 2π√(((ML2)/12 + Mx2)/gML) = 2π√((L2/12+x2)/gL).

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