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
.
We can use the formula for the period of the pendulum to find the approximate length of the pendulum.
The formula is given as:
T ≈ 2π√(L/g)
Here, T is the period of the pendulum, L is the length of the pendulum, and g is the gravitational constant.
Given that the period is 2 seconds and the gravitational constant is 9.8 m/s^2, we can plug these values into the formula and solve for L.
2 = 2π√(L/9.8)
Dividing both sides by 2π, we get:
1 = √(L/9.8)
Squaring both sides, we get:
1^2 = (L/9.8)
1 = L/9.8
L = 9.8
Therefore, the approximate length of the pendulum is 9.8 meters.
To find the length of the pendulum, we can rearrange the formula for the period:
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
Let's isolate the length, L, by multiplying both sides of the equation by 9.8:
2 * 9.8 ≈ 2𝜋√𝐿
19.6 ≈ 2𝜋√𝐿
Now, divide both sides of the equation by 2𝜋:
19.6 / (2𝜋) ≈ √𝐿
To find the length, we need to square both sides of the equation:
(19.6 / (2𝜋))^2 ≈ 𝐿
Calculating this expression gives us:
(19.6 / (2𝜋))^2 ≈ 𝐿
L ≈ 9.9 meters
Therefore, the approximate length of the pendulum is 9.9 meters.