**How does the string length of a pendulum affect the period of a pendulum?**

**Evette Martinez**

3rd period AP Physics

Mrs. Ballard

8/4/14

3rd period AP Physics

Mrs. Ballard

8/4/14

Background Physics

a.) Concepts explained:

Pendulums consist of a bob which is the weight

attached at the bottom of a string. The weight swings freely when suspended from a pivot. Once a pendulum has been displaced from its equilibrium point at an angle in any direction, gravity will cause it to accelerate back towards its equilibrium point. Galileo Galilei discovered the pendulum as an instrument of keeping time.

b.) Equations explained:

For small amplitudes, the following equation can be used to determine the time without having to do trials :

T is the time of a the pendulums period.

L is the length of the pendulum in meters.

G is the acceleration due to gravity, which at sea level is 9.81 m/s.

G can also be calculated as :

M is the mass of the Earth.

R is the radius of the Earth.

a.) Hypothesis:

If the length of several pendulums are tested, then the longest string will take the most time to complete one pendulum period.

b.) Variables:

The independent variable is the length of the pendulum string.

The dependent variable is the time it takes for the pendulum to reach one extreme and back.

The controls are the amplitude in which the pendulum is dropped each time, and the weight of the bob.

c.) Experiment Description

c.) Experiment description

The period of a pendulum will be compared by being calculated in two different ways. It will be calculated by the formula, and it will be tested in the experiment with a stop watch. The bob was made up 3 washers tied together. Several pendulums of the same mass were dropped at equivalent angles and timed to see how long it took for the pendulum to swing from the position it was dropped, to one extreme, and back. The pivot in which the pendulums swung from was a metal pole that was supported on both sides by books of the same height. The lengths tested were 10, 20, 40 and 60 cm.

d.) Results

I got my data from both my experiment, and using the equation to formulate accurate answers.

From Experiment:

From Equation:

Conclusion

a.) Implications

The results showed that the time it took for the pendulum to reach one extreme and back was longer , the longer the string the bob was attached to was. This proved that if the pendulum string was longer, then the pendulum period would be longer as well.

b.) Applications

Pendulums must have a certain length, mass, and extreme to be used for clocks. Pendulums are not typically used in clocks today, but are used for city hall clocks and antique pieces.

c.) So What?

If a pendulum does not have the correct measurements, time cannot correctly be shown or presented.