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

A pendulum swings with a maximum angle of 30 degrees. What is the approximate time period for small angles? (2022)

A pendulum swings with a maximum angle of 30 degrees. What is the approximate time period for small angles? (2022)

Step 1: Understand that the time period (T) of a pendulum can be calculated using the formula T ≈ 2π√(L/g).
Step 2: Identify the variables in the formula: L is the length of the pendulum, and g is the acceleration due to gravity (approximately 9.8 m/s²).
Step 3: Assume the length of the pendulum (L) is 1 meter for this calculation.
Step 4: Substitute L = 1 m and g = 9.8 m/s² 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 by 2π (approximately 6.283): T ≈ 6.283 * 0.319 ≈ 2.0 seconds.
Step 8: Conclude that the approximate time period for the pendulum swinging at a maximum angle of 30 degrees is about 2.0 seconds.

Pendulum Motion – The time period of a simple pendulum is determined by its length and the acceleration due to gravity, particularly for small angle approximations.
Small Angle Approximation – For small angles (typically less than 15 degrees), the sine of the angle can be approximated by the angle itself in radians, simplifying calculations.