# Answer on Mechanics | Relativity Question 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

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=(ML

^{2})/3.

So

T = 2π/ω = 2π√(I/gML) = 2π√(((ML

^{2})/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=(ML

^{2})/12+Mx

^{2}.

And we have

T = 2π/ω = 2π√(I/gML) = 2π√(((ML

^{2})/12 + Mx

^{2})/gML) = 2π√((L

^{2}/12+x

^{2})/gL).

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