A pendulum swings with a maximum angle of 15 degrees. What is the approximate fr

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Question: A pendulum swings with a maximum angle of 15 degrees. What is the approximate frequency of the pendulum if its length is 1 m? (2020)

Options:

Correct Answer: 1 Hz

Exam Year: 2020

Solution:

Frequency (f) = 1 / (2π√(L/g)) = 1 / (2π√(1/9.8)) ≈ 1 Hz.

A pendulum swings with a maximum angle of 15 degrees. What is the approximate frequency of the pendulum if its length is 1 m? (2020)

A pendulum swings with a maximum angle of 15 degrees. What is the approximate frequency of the pendulum if its length is 1 m? (2020)

Step 1: Identify the formula for the frequency of a pendulum, which is f = 1 / (2π√(L/g)).
Step 2: Determine the length (L) of the pendulum, which is given as 1 meter.
Step 3: Identify the acceleration due to gravity (g), which is approximately 9.8 m/s².
Step 4: Substitute the values into the formula: f = 1 / (2π√(1/9.8)).
Step 5: Calculate the value inside the square root: 1/9.8 ≈ 0.10204.
Step 6: Find the square root of 0.10204, which is approximately 0.319.
Step 7: Multiply this value by 2π: 2π * 0.319 ≈ 2.006.
Step 8: Finally, take the reciprocal to find the frequency: f ≈ 1 / 2.006 ≈ 0.498 Hz, which is approximately 1 Hz.

Pendulum Motion – The behavior of a pendulum, including its frequency and the factors affecting it, such as length and gravitational acceleration.
Frequency Calculation – The formula for calculating the frequency of a simple pendulum based on its length and the acceleration due to gravity.