The period, T, of a pendulum can be approximated by the formula ≈ 2𝜋√𝐿/𝑔, where L is the

Question

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 T.

T ≈ 2𝜋√𝐿/𝑔

Given that the period T is 2 seconds and the gravitational constant g is 9.8 m/s^2, we can substitute these values into the formula:

2 ≈ 2𝜋√𝐿/9.8

Dividing both sides of the equation by 2𝜋/9.8:

2/2𝜋 ≈ √𝐿/9.8

Simplifying:

1/𝜋 ≈ √𝐿/9.8

To isolate 𝐿, we can square both sides of the equation:

(1/𝜋)^2 ≈ (√𝐿/9.8)^2

1/𝜋^2 ≈ 𝐿/9.8

Multiplying both sides of the equation by 9.8:

9.8/𝜋^2 ≈ 𝐿

So, the approximate length of the pendulum is 9.8/𝜋^2.