Theoretical part

Will consider oscillation of peg, position of axis of which, it is possible to change along a peg. Such peg shows by itself a physical pendulum. The period of oscillation of the physical pendulum is determined by formula

, (8.1)

Where I is a moment of inertia of peg, m is mass, a is distance from the axis of rotation to the center of the masses, g is the free fall acceleration. The moment of inertia I in this case is determined on the theorem of Steiner:

, (8.2)

where I₀ is a moment of inertia of peg in relation to an axis which go athwart to the peg through his center:

(8.3)

After a substitution (8.2) and (8.3) in a formula (8.1) get:

(8.4)

In the formula (8.4) the size a can change in the interval: .

1. At , period , that at fixing of peg in a center of peg it will not oscillate in general, in this case the total moment of forces which operate on a peg in any its position will equal a zero.

2. At for T get:

(8.5).

Figure 8.1

3. Research of formula (8.4) shows on the extremum, that a function has minimum, a coordinate of which is from a condition . After differentiation (8.4) find, that a function has minimum at

, (8.6)

or approximately at .

For experimental research of dependence of period of oscillations of peg from position of axis of rotation a device, represented on fig. 8.1, is used. If peg 1 to set a supporting prism 2 on a bracket 3, to show out of position of equilibrium on some corner and to release, then he will carry out oscillation in relation to position of equilibrium.