Give the expression for Time Period of Compound Pendulum.
The time period (\(T\)) of a compound pendulum, denoting the time for one complete oscillation, can be determined using the formula:
\[T = 2\pi \sqrt{\frac{I}{m \cdot g \cdot L}}\]
where \(I\) represents the moment of inertia, \(m\) is the mass, \(g\) is the acceleration due to gravity, and \(L\) signifies the length of the pendulum.
ANSWER : The time period (T) of a compound pendulum refers to the time it takes for one complete oscillation or swing. It depends on the length (\(L\)) of the pendulum, the acceleration due to gravity (\(g\)), and the moment of inertia (\(I\)) of the pendulum about its axis of rotation.
The formula for the time period (\(T\)) of a compound pendulum is given by :
\[T = 2\pi \sqrt{\frac{I}{m \cdot g \cdot L}}\]
where :
- \(T\) is the time period of the compound pendulum in seconds.
- \(\pi\) (pi) is a constant approximately equal to 3.14159, representing the ratio of a circle's circumference to its diameter.
- \(\sqrt{}\) denotes the square root function, which gives the positive square root of the value inside the parentheses.
- \(I\) is the moment of inertia of the compound pendulum about its axis of rotation.
- \(m\) is the mass of the pendulum in kilograms.
- \(g\) is the acceleration due to gravity, approximately 9.81 m/s\(^2\) on Earth.
- \(L\) is the length of the pendulum in meters, measured from the point of rotation to the center of mass of the pendulum.
In summary, the time period of a compound pendulum can be determined by its moment of inertia, mass, length, and the acceleration due to gravity. A longer pendulum or a larger moment of inertia will result in a longer time period for one complete oscillation.
Also Read : Write Lenz's Law.
Also Read : State Stoke's Law.
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