The Angular Frequency Of A Simple Pendulum Depends On Its Length And On The Local Acceleration Due To Gravity.
The Correct Answer and Explanation is :
The rate at which the angular displacement (θ) of a simple pendulum changes with respect to time (dθ/dt) is known as its angular velocity. This quantity is directly related to the pendulum’s angular frequency (ω), which determines how quickly the pendulum oscillates.
Angular Frequency and Its Dependence on Length and Gravity
For a simple pendulum undergoing small oscillations, the angular frequency (ω) is given by:
[ \omega = \sqrt{\frac{g}{L}} ]
Where:
- ( g ) is the acceleration due to gravity, and
- ( L ) is the length of the pendulum.
This formula indicates that the angular frequency depends on both the length of the pendulum and the local acceleration due to gravity. Specifically, increasing the length ( L ) decreases the angular frequency (leading to slower oscillations), while increasing the gravitational acceleration ( g ) increases the angular frequency (leading to faster oscillations).
Determining the Correct Answer
Given the options provided:
- OA.
- OB.
- EL OC.
- 20 E 4XLTA O E.
- None Of The Above.
It appears that the options are not clearly defined or may contain typographical errors. Without proper context or clarification of these options, it’s challenging to determine the correct answer. If you could provide more details or correct any potential errors in the options,
Conclusion
Understanding the relationship between a simple pendulum’s angular frequency, its length, and the local acceleration due to gravity is fundamental in physics. The angular frequency is inversely proportional to the square root of the length and directly proportional to the square root of the gravitational acceleration. If you can provide more information or clarify the options, I would be glad to offer a more precise answer.