A pendulum swings with a period of 1 second. What is the length of the pendulum?

A pendulum swings with a period of 1 second. What is the length of the pendulum?

Step 1: Understand the formula for the length of a pendulum, which is L = (gT^2)/(4π^2).
Step 2: Identify the values needed for the formula. Here, T (the period) is given as 1 second, and g (the acceleration due to gravity) is approximately 9.8 m/s².
Step 3: Substitute the values into the formula. Replace T with 1 and g with 9.8: L = (9.8 * 1^2)/(4 * π^2).
Step 4: Calculate 1^2, which is 1. So the formula simplifies to L = (9.8 * 1)/(4 * π^2).
Step 5: Calculate the denominator, which is 4 * π^2. π is approximately 3.14, so π^2 is about 9.86. Therefore, 4 * π^2 is about 39.44.
Step 6: Now divide 9.8 by 39.44 to find L. This gives you L ≈ 0.248 m.
Step 7: Since we want the length in meters, we can round it to approximately 1 meter for simplicity.

Pendulum Motion – The relationship between the period of a pendulum and its length, derived from the formula T = 2π√(L/g).
Gravitational Acceleration – Understanding the value of gravitational acceleration (g) as approximately 9.8 m/s² on the surface of the Earth.
Mathematical Manipulation – Applying algebraic manipulation to derive the length of the pendulum from the period.