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2- Physical Pendulum: If a hanging object oscillates about an axis that does not pass through its center of mass and the object cannot be approximated as a point mass, then the kind of pendulum is called a physical pendulum. A typical form of physical pendulum is as shown in the figure below.
The acceleration of the physical pendulum is given by,
Here, we have assumed that the angle θ is very small. Since the acceleration of the physical pendulum is directly proportional to the displacement in opposite direction, the oscillation of the pendulum is simple harmonic. And, the period of oscillation is given as:
where, the angular frequency ω is given by,
Thus, the time period of the physical pendulum depends upon the moment of inertia, mass, acceleration due to gravity and the value of d.
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Waves and Optics