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17, January 2022

Pendulum Periods

By: Jackson Widener

Jeremy

Sixto

Eric

Introduction:

Suspending a piece of mass at the end of a string creates a simple pendulum structure.The motion caused by a slight push will create disturbance and a this represents a simple harmonic motion.Simple harmoninc motion is the to and fro movement ascillatory motion.The time taken to return to a particular position is referred to as a period.Gravity is one of two main forces acting upon a pendulum.

Purpose:

Finding the Value of g (force of gravity) using a simple pendulum.

Diagram:

Data:

Amplitude: 100g & 1m

Amplitude (o)	Period (s)	Average (s)
5	2.00	2.00	2.01	2.01	2.01
10	2.03	2.06	2.01	2.04	2.03
15	1.88	2.03	2.03	2.00	1.99
20	2.03	2.02	2.02	2.01	2.02
25	2.04	2.03	2.02	2.02	2.03
30	2.05	2.02	2.11	2.05	2.06

Length: 100g & 25o

Length (m)	Period (s)	Average (s)
0.5	1.33	1.42	1.38	1.44	1.39
0.6	1.57	1.57	1.58	1.58	1.58
0.7	1.71	1.69	1.84	1.72	1.74
0.8	1.82	1.85	1.82	1.80	1.82
0.9	1.93	1.89	1.94	1.92	1.92
1.0	2.03	2.02	2.05	2.04	2.04

Mass: 0.5m & 25o

Mass (g)	Period (s)	Average (s)
100	1.45	1.43	1.44	1.45	1.44
200	1.47	1.45	1.48	1.45	1.46
300	1.44	1.44	1.46	1.43	1.44

Conclusion / Discussion:

In this experiment we measured the value of g=10.307 m/s2.

4.821% error as compared to the undisputed g=9.81m/s2

We conclude that the value of gravity measured by this experiment to be 10.307m/s2 with an uncertainity of + 0.497m/s2.We can also conclude that the pendulum traverses a longer distance in a shorter period, than in a shorter distance because its period is shorter.

Questions:

1.​Why is Logger Pro set up to report the time between every other blocking of the Photogate? Why not the time between every block?

To complete a full cycle the pendulum must enter and exit the photogate for once, that is why the logger pro has set up to report the time between every other blocking of the photogate instead of the time between every block.

2.​Using either Graphical Analysis or graph paper, plot a graph of pendulum period vs. amplitude in degrees. Scale each axis from the origin (0,0). Does the period depend on amplitude? Explain.

The Period increases as the amplitude increases. It is because as the amplitude increases the pendulum goes farther and thus the time period also increases.

3.​Using either Graphical Analysis or graph paper, plot a graph of pendulum period T vs. length l. Scale each axis from the origin (0,0).  Does the period appear to depend on length?

The period of the pendulum depends on the length. As the length increase the period also increases. That is the longer the length of the string the longer the period will be.

4.​Using either Graphical Analysis or graph paper, plot the pendulum period vs. mass. Scale each axis from the origin (0,0). Does the period appear to depend on mass? Do you have enough data to answer conclusively?

Since the number of data points are less, we can not conclude anything from this graph. But the period seems to be independent of the mass.

5.​To examine more carefully how the period T depends on the pendulum length l, create the following two additional graphs of the same data: T 2 vs. l and T vs. l 2. Of the three period-length graphs, which is closest to a direct proportion; that is, which plot is most nearly a straight line that goes through the origin? 

It can be clearly seen that of the three period - length graphs the graph which plots T^2 vs. L is most nearly a straight line. That is T^2 is directly proportional to the length L.

6.​Using Newton’s laws, we could show that for some pendulums, the period T is related to the length l and free-fall acceleration g by

T = 2π√ L / g , or  T2 = (4π2 / g) * L

​Does one of your graphs support this relationship?

Yes. T2 is directly proportional to L. Therefore the graph of T2 vs L supports this relationship

7.​From your graph of T2 vs. l, determine a value for g. 

T2 = (4π2 / g) * L from the plotting the gradient is 3.83 and we know gradient =(4π2 / g)

Therefore g = (4π2 / 3.83)= 10.307 m/s2