Question

A pendulum is made from a thin homogeneous metal plate cut into an equilateral triangle. What is the frequency of small oscillations if the plate is suspended by one vertex? What is the frequency for the same plate suspended at a midpoint of one of the edges? For both cases assume that the oscillation is in the plane of the plate.

Answer 1

T = Time period of physical pendulum

I Support = moment of inertia about vertex = 5ml^2/12, , m= mass, l = side of triangle

Lcm = position of center of mass with respect to vertex = Sqrt(3) l/3

T =

(b)

Moment of inertia about middle of a side = 5ml^2/12 + m [ (sqrt3)l/2]^2

= 5ml^2/12 + 3ml^2/4 =14 ml^2/12 = (7/6) ml^2

Distance to cm = (sqrt2)l/6