The period, T, of a pendulum can be approximated by the formula ≈ 2𝜋√𝐿/𝑔, where L is the length of the pendulum and g is the gravitational constant. What is the approximate length of the pendulum if it has a period of 2 s? Note: On Earth the gravitational constant is 9.8 m/s2.

Answer 1

To find the approximate length of the pendulum, we can rearrange the formula for the period as follows:

T ≈ 2𝜋√𝐿/𝑔

Let's plug in the given values and solve for L:

2 s ≈ 2𝜋√L/9.8 m/s^2

Divide both sides of the equation by 2𝜋:

2 s / 2𝜋 ≈ √L/9.8 m/s^2

Square both sides of the equation to eliminate the square root:

(2 s / 2𝜋)^2 ≈ L/9.8 m/s^2

(4s^2 / 4𝜋^2) ≈ L/9.8 m/s^2

Multiply both sides of the equation by 9.8 m/s^2:

9.8 m/s^2 * (4s^2 / 4𝜋^2) ≈ L

L ≈ 9.8 m/s^2 * (4s^2 / 4𝜋^2)

Simplify the equation:

L ≈ (9.8 * 4s^2) / (4𝜋^2)

L ≈ (9.8 * 4s^2) / (4 * 3.14^2)

L ≈ (39.2s^2) / (39.478)

L ≈ s^2

Therefore, the approximate length of the pendulum is s^2, where s is the period of 2 seconds.