Basic Pendulums Period^2 vs distance

  • Thread starter Saristine
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In summary, during class, we tested the period of different lengths of pendulums and graphed the squared period against the distance, resulting in a slope of 3.974 s^2/m. We were told that this is close to a constant and asked to find out what it is and its significance. After searching online, the equation for the period of a simple pendulum was found, which can be rearranged to show that the squared period is equal to a constant times the length of the pendulum. This constant is what we were asked to find and it closely matches the measured slope.
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Saristine
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In class we tested the period of different lengths of pendulums. When we squared the period and graphed it against the distance it caused a slope of 3.974 s^2/m. We kept the angles under 15 degrees. We were told that this is close to a constant and asked to figure out what that constant is and what it means, but i can not for the life of me find it in our textbook or on the internet.
Thanks in advance.

--Saristine
 
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  • #2
Saristine said:
In class we tested the period of different lengths of pendulums. When we squared the period and graphed it against the distance it caused a slope of 3.974 s^2/m. We kept the angles under 15 degrees. We were told that this is close to a constant and asked to figure out what that constant is and what it means, but i can not for the life of me find it in our textbook or on the internet.
Thanks in advance.

--Saristine

I just Googled "period of simple pendulum" and immediately came upon this:

http://en.wikipedia.org/wiki/Pendulum#Period_of_oscillation

Equation 1 tells you everything you need. (By the way, I find it hard to believe this wouldn't have been covered in your class.) What happens if you square both sides of the equation? You end up with something in the form:

T2 = const. * L

What is the constant supposed to be according to the formula? How does this compare to your measured slope?
 

What is a basic pendulum?

A basic pendulum is a simple mechanical system that consists of a weight suspended from a fixed point by a string or rod. When the weight is pulled to one side and released, it will swing back and forth in a regular pattern.

What is the period of a pendulum?

The period of a pendulum is the time it takes for one complete swing, from one side to the other and back again. It is typically measured in seconds.

What is the relationship between the period of a pendulum and its distance from the pivot point?

The relationship between the period of a pendulum and its distance from the pivot point is that they are inversely proportional. This means that as the distance from the pivot point increases, the period of the pendulum will also increase.

How is the period of a pendulum calculated?

The period of a pendulum can be calculated using the formula T = 2π√(L/g), where T is the period in seconds, L is the length of the pendulum in meters, and g is the acceleration due to gravity, which is approximately 9.8 m/s² on Earth.

Why does the period of a pendulum increase as the distance from the pivot point increases?

The period of a pendulum increases as the distance from the pivot point increases because the longer the pendulum, the greater the distance it has to travel in one swing. This increases the time it takes for the pendulum to complete one swing.

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