Simple Pendulum Lab Report, Cheat Sheet of Physics

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The Simple Pendulum

 - PHYS - Lab 

• October 2 5 ,
• Noah Wagner,

Introduction:

In this lab we will be looking at the simple pendulum, specifically the oscillation period

independent of the oscillation amplitude, oscillation period independent of the oscillating mass.

These oscillations are given by the equation, 𝑇 = 2 𝜋%

!

"

. This equation is how we determine the

oscillation period of a simple pendulum under these conditions. We can also use the parameters

of the experiment to determine this as well.

Procedure:

The procedure set up required a textbook/ weight, tooth floss, binder clip, protractor,

multiple of the same type of coin and a timing device. To set up the experiment I attached the

tooth floss to the binder clip and inserted coins into the binder clip. I then inserted the tooth floss

into the pages of a textbook to hold the binder clip over the edge of a desk. With this set up I

would take the binder clip and move it to the side, with tension on the tooth floss, to a certain

angle using the protractor then would release it and start timing after the first oscillation. For the

first part of the experiment the same number of coins (weight) were used at different oscillation

angles each time, the second part was changing the amount of coins but keeping the same

oscillation angle, and the third part was changing the pendulum length while keeping the amount

of coins and oscillation angle the same. The setup is shown in Fig 1, Fig 2 and Fig 3.

Fig 3. Set up of the experiment, using the protractor.

Data:

Oscillation Angle

q (°)

Time for 10 Oscillations

t (sec)

Period

T ± (s)

Pendulum length L = (0.059 ± 0.001) m

Pendulum mass m = (0.018 ± 0.004) kg

Fig 4. Data of the period vs. oscillation amplitude trial.

Pendulum mass

(kg)

Time for 10 Oscillations

t (sec)

Period

T ± (s)

8.80e- 3 15.4 2 1.5 4 ± 0.0 2

1.32e- 2 15. 1.5 3 ± 0.0 2

1.76e- 2 15. 1.5 5 ± 0.0 2

2.20e- 2 15. 1.5 6 ± 0.0 2

2.64e- 2 15. 1.5 7 ± 0.0 4

3.08e- 2 15. 1.5 8 ± 0.0 4

Pendulum length L = (0.059 ± 0.01) m

Oscillation angle q = 45°

Fig 6. Data table representing the period vs. pendulum mass.

Pendulum length

(m)

Time for 10 Oscillations

t (sec)

Period

T ± (s)

4.9e- 1 13.

1. 38 ± 0.0 4

5.1e- 1 14.

1. 44 ± 0.0 0

5.3e- 1 15. 08

1. 51 ± 0.

5.5e- 1 1 4.

1. 50 ± 0.0 4

5.7e- 1 15. 30

1. 53 ± 0.0 0

5.9e- 1 15. 78

1. 58 ± 0.0 2

6.1e- 1 15. 1.59 ± 0.

6.3e- 1 15. 1.58 ± 0.

6.5e- 1 16. 1.63 ± 0.

6.7e- 1 16. 1.66 ± 0.

Pendulum mass m = (0.018± 0.004) kg

Oscillation angle q = 45°

Fig 7. Data table representing the pendulum length vs. period.

Fig 9. Graph of pendulum length vs. period with a curved fit graphical representation.

Analysis / Discussion:

For the analysis of Statement 1: The oscillation period of a simple pendulum is

independent of the oscillation amplitude is proven and is not violated. As seen in both Fig 4 and

Fig 5 the periods range from 1.51 s-1.54 s, excluding the first and last points. Therefore, we can

argue that the data from the trial ( Fig 4 and Fig 5 ) do not violate statement one for the oscillation

angles of 5°- 25 °, and the proposed theory has survived the test.

Statement 2: The oscillation period of a simple pendulum is independent of the oscillating

mass, is proven and not violated. Although the period seems to increase as weight is added, the

increase excluding the first and last data points is from 1.53 s – 1.57 s, which ultimately comes

down to human error as that fraction of time is so small. This is represented in Fig 6, showing

that statement 2 is not violated for the masses of 8.80g - 30.8g, and the proposed theory has

survived the test. All quarters used were from 2000 – present. See Sample Calculations for the

calculation of weights.

Statement 3: The oscillation period of the simple pendulum is given by the equation:

!

"

. This statement is not violated as the oscillation period increases with the length of

the pendulum. This is seen in the data table Fig 7. This can also be seen through the equation

given:

If we use the length of 5.3e-2 and 6.1e-2 from Fig 7 we can plug them into the equation and

further prove the statements validity,

5. 3 × 10

#$

%

And,

6. 1 × 10

#$

%

This shows that theoretically the period should increase as the length of the pendulum increases

and it is seen in the experiment as well, further proving the validity of the statement. In this case

the linear fit represents the data better as it is easier to dissect as well as the slope is directly

Questions:

1. Time for 10 oscillations: 14.52s

To find the period T:

𝑡 10 𝑜𝑠𝑐𝑖𝑙𝑙𝑎𝑡𝑖𝑜𝑛𝑠 ÷ 10 = 𝑇

14. 52 𝑠 ÷ 10 = 𝑇

Then plug T in to find L:

%

The length of the pendulum in that video is 0.52m or 52cm.

2. To find oscillation period of the video on the moon we use the length found above and

use the gravitational force od the moon in the equation above:

%

The period of oscillation on the moon is 3.56 seconds.

Sample Calculations:

Determining period from the time of 10 oscillations (data point 1 from Fig 4 ):

÷ 10 = 𝑇

15. 76 𝑠 ÷ 10 = 𝑇

The period is 1.58 ± 0.04 s.

Calculating the weight of the coins from Fig 6 data point 1:

&'()

'+,

'+,

'+,

Determining period in statement 3 (data point 3 in Fig 7 ):

5. 3 × 10

#%

%

5. 3 × 10

#%

%