Final answer:
The frequency of oscillation for a circular annulus can be found by treating it as a physical pendulum and using the distance from the pivot to the center of mass, along with the gravitational constant, in the frequency formula.
Step-by-step explanation:
To find the frequency of oscillation of a circular annulus in small oscillations, we can model it as a physical pendulum. The frequency of a physical pendulum is given by the formula:
f = (1/2π) ∙ √(g / l)
where g is the acceleration due to gravity (9.8 m/s2) and l is the distance from the pivot to the center of mass.
For a circular annulus, the center of mass is located at the radius halfway between the inner and outer radii. So l can be calculated as (49.2 cm + 36.2 cm) / 2 = 42.7 cm. After converting this to meters, we can find the frequency.
The mass of the annulus (15g) is not needed in the frequency calculation but can be required when determining the moment of inertia or other dynamics of the system. Frequencies are typically measured in Hertz (Hz) which is equivalent to oscillations per second.
To get the answer, the detailed calculations with the substitution of the correct value of l should be performed:
f = (1/2π) ∙ √(9.8 m/s2 / 0.427 m)
Calculate the square root and divide by 2π to find the frequency of the oscillation.