A pendulum swings with a maximum angle of 30 degrees. What is the approximate pe

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Question: A pendulum swings with a maximum angle of 30 degrees. What is the approximate period of the pendulum if its length is 1 m?

Options:

Correct Answer: 2.0 s

Solution:

The period T of a simple pendulum is given by T = 2π√(L/g). Here, L = 1 m and g = 9.8 m/s². Thus, T = 2π√(1/9.8) ≈ 2.0 s.

A pendulum swings with a maximum angle of 30 degrees. What is the approximate period of the pendulum if its length is 1 m?

A pendulum swings with a maximum angle of 30 degrees. What is the approximate period of the pendulum if its length is 1 m?

Step 1: Identify the formula for the period of a simple pendulum, which is T = 2π√(L/g).
Step 2: Determine the length of the pendulum (L). In this case, L = 1 meter.
Step 3: Identify the acceleration due to gravity (g). The standard value is g = 9.8 m/s².
Step 4: Substitute the values of L and g into the formula: T = 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 result by 2π (approximately 6.283): T ≈ 6.283 * 0.319.
Step 8: Calculate the final result: T ≈ 2.0 seconds.

Pendulum Motion – Understanding the relationship between the length of a pendulum, gravitational acceleration, and its period.
Period Formula – Application of the formula T = 2π√(L/g) to calculate the period of a pendulum.
Small Angle Approximation – Recognizing that the formula is derived under the assumption of small angles, though 30 degrees is close enough for approximation.