Question

A physical pendulum in the form of a planar object moves in simple harmonic motion with an unknown frequency. The pendulum has a mass of 2.5 kg, and the pivot is located at a distance d=0.5 m from the center of mass. The moment of Inertia of the pendulum is 0.6 kg⋅m². Determine the value of the unknown frequency.

Answer 1

The frequency of a physical pendulum can be found by calculating the period using the given mass, moment of inertia, and distance to the pivot, and then finding the reciprocal of the period.

Step-by-step explanation:

To determine the frequency of a physical pendulum undergoing simple harmonic motion, we can use the formula for the period T of a physical pendulum:

T = 2π √(I / (m · g · d)),

where I is the moment of inertia, m is the mass, g is the acceleration due to gravity, and d is the distance from the pivot to the center of mass. Given that the moment of inertia I is 0.6 kg·m², the mass m is 2.5 kg, the distance d is 0.5 m, and taking g as 9.8 m/s², we can solve for T and then find the frequency f which is the reciprocal of the period T.