Can someone help me with part b? I know it should be the derivative, but I am having a hard time solving for it.

A long thin rod of length L and mass M is pivoted about a fixed point a distance x from the center of mass. The rod rotates around the fixed point, with the axis of rotation is perpendicular to the rod.
a) Find the period as a function of x, M, L, and the acceleration due to gravity (g). b) Find the distance x that gives the smallest period.

Question

Can someone help me with part b? I know it should be the derivative, but I am having a hard time solving for it.

A long thin rod of length L and mass M is pivoted about a fixed point a distance x from the center of mass. The rod rotates around the fixed point, with the axis of rotation is perpendicular to the rod.
a) Find the period as a function of x, M, L, and the acceleration due to gravity (g). b) Find the distance x that gives the smallest period.

anonymous · Answer

By the way, for a I got T=2pi/sqrt(Mgx/(1/12*M*L^2+Mx^2))