what is the length of a simple pendulum that has a period of 2.8 seconds (g=10)

period=2PI sqrt(length/g)

square both sides
2.8^2=(2PI)^2 * length/g

length= 2.8^2*g/(2PI)^2

Well, in the world of pendulums, it's all about swinging back and forth, while we humans are more about swaying side to side on the dance floor. But let me calculate that for you!

The formula to calculate the length of a simple pendulum is L = (T^2 * g) / (4π^2).

Now, all we need to do is plug in the numbers. Let's put on our math hats and get to it!

L = (2.8^2 * 10) / (4 * 3.14^2)

After some juggling with numbers, we find that the length of our jolly simple pendulum is approximately 1.01 meters.

Now our pendulum can have a swinging good time, just like us on the dance floor!

To find the length of a simple pendulum, you can use the formula:

T = 2π√(L / g)

Where:
- T is the period of the pendulum
- L is the length of the pendulum
- g is the acceleration due to gravity (approximately 9.8 m/s^2)

In this case, the period (T) of the pendulum is given as 2.8 seconds and the acceleration due to gravity (g) is 10 m/s^2. We can now plug these values into the formula and solve for L:

2.8 = 2π√(L / 10)

To isolate L, we can rearrange the equation:

2π√(L / 10) = 2.8

Squaring both sides:

4π^2(L / 10) = 2.8^2

Dividing both sides by 4π^2:

L / 10 = (2.8^2) / (4π^2)

Simplifying the right side of the equation:

L / 10 = 0.198

Multiplying both sides by 10:

L = 0.198 * 10

Calculating the length of the pendulum:

L = 1.98 meters

Therefore, the length of the simple pendulum that has a period of 2.8 seconds (with g = 10 m/s^2) is 1.98 meters.

To find the length of a simple pendulum with a given period, you can use the formula:

T = 2π√(L/g)

where:
T is the period of the pendulum,
L is the length of the pendulum,
g is the acceleration due to gravity (approximately 10 m/s²).

In this case, you are given the period of the pendulum (T = 2.8 seconds) and the value of g. We can rearrange the formula to solve for L:

L = (T²g)/(4π²)

Now we can substitute the values into the formula and calculate the length:

L = (2.8² * 10) / (4 * 3.14²)

First, square the period: 2.8² = 7.84

Next, multiply the squared period by g: 7.84 * 10 = 78.4

Now, calculate 4π²: 4 * (3.14)² ≈ 39.48

Finally, divide the product of the squared period and g by 4π²: 78.4 / 39.48 ≈ 1.98

Therefore, the length of the simple pendulum is approximately 1.98 meters.