The Period T, in seconds, of a pendulum depends on the distance, L, in meters, between the pivot and the pendulum's centre of mass. If the initial swing angle is relatively small, the period is given by the radical function T=2pi(sqrtL/g) where g represents acceleration due to gravity (approximately 9.8m/s^2 on Earth.) Jeremy is building a machine and needs it to have a pendulum that takes 1 second to swing from one side to the other how long should the pendulum be, in centimeters?

The full period is 2 seconds.

Divide 2 / 2 x Pi. Square this equation so you have 4 / 4 Pi squared. Then times that answer by 980 (9.8 m to Cm)

You should get the correct answer of approximately 99 Cm for L

To find the length of the pendulum, we can use the equation provided:

T = 2π√(L/g)

Given that T = 1 second and g = 9.8 m/s^2, we can substitute these values into the equation:

1 = 2π√(L/9.8)

To solve for L, we need to isolate it by rearranging the equation:

√(L/9.8) = 1 / (2π)

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

L/9.8 = (1 / (2π))^2

L/9.8 = 1 / (4π^2)

Now, let's solve for L:

L = (9.8 / (4π^2)) * 1

L = 0.248 meters

Since you're looking for the length in centimeters, we can convert it:

Length = 0.248 * 100

Length ≈ 24.8 centimeters

Therefore, the pendulum should be approximately 24.8 centimeters long.

To find the length of the pendulum, we can rearrange the formula T=2π(√L/g) to solve for L.

Given:
T = 1 second
g = 9.8 m/s² (acceleration due to gravity on Earth)

Let's substitute these values into the equation and solve for L:

1 = 2π(√L/9.8)

To isolate √L, we can divide both sides of the equation by 2π:

1 / (2π) = (√L/9.8)

Next, we can multiply both sides of the equation by 9.8:

(9.8 / (2π)) = √L

Now, let's square both sides of the equation to eliminate the square root:

[(9.8 / (2π))]² = L

Calculating this expression:

[(9.8 / (2π))]² ≈ 1.565

Therefore, L ≈ 1.565 meters.

Since the question asks for the length in centimeters, we need to convert the length from meters to centimeters:

1 meter = 100 centimeters

So, L ≈ 1.565 meters * 100 ≈ 156.5 centimeters.

Therefore, the pendulum should have a length of approximately 156.5 centimeters.

in MKS units,

1 = 2π√(L/9.8)
(1/2π)^2 = L/9.8
L = 9.8/(2π)^2 = ...
convert to cm