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.
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Expert's answer
2011-06-23T17:09:25-0400
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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