The period, T, of a pendulum can be approximated by the formula ≈ 2𝜋√𝐿𝑔, 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

We can rearrange the formula for the period of a pendulum to solve for the length of the pendulum, L:
T ≈ 2𝜋√𝐿𝑔

Dividing both sides of the equation by 2𝜋√𝑔 gives:
T / (2𝜋√𝑔) ≈ √𝐿

Now, we can substitute the given values for the period and gravitational constant:
2s / (2𝜋√(9.8m/s²)) ≈ √𝐿

Simplifying:
1 / (√(9.8𝜋)) ≈ √𝐿

To find the approximate length of the pendulum, we square both sides of the equation:
1 / (√(9.8𝜋))² ≈ 𝐿

Simplifying further:
1 / (9.8𝜋) ≈ 𝐿

Thus, the approximate length of the pendulum is 1 / (9.8𝜋) meters.