Question

A physical pendulum has an oscillation frequency of f. A doubling of the the rotational inertia of the system (with all other parameters unchanged) would change the frequency. Would it increase or decrease?

Answer 1

For physical pendulum,frequency of oscillation is given by:

f=[1/(2)]*(mgd/I)^1/2  where f is frequency of oscillation, m is mass of the physical pendulum, g is gravitational acceleration,d is distance of center of mass from the pivot point, I is moment of inertia.

Clearly, from the above formula, if moment of inertia I is increased with all other parameters unchanged, frequency f decreases.

So,if moment of inertia is doubled with all other parameters unchanged, frequency of oscillation would decrease.