Pendulum Periods
Name: Date:
A swinging pendulum keeps a very regular beat. It is so regular, in fact, that for many years the pendulum was the heart of clocks used in astronomical measurements at the Greenwich Observatory.
There are at least three things you could change about a pendulum that might affect the period (the time for one complete cycle):
the amplitude of the pendulum swing
the length of the pendulum, measured from the center of the pendulum bob to the point of support
the mass of the pendulum bob
To investigate the pendulum, you need to do a controlled experiment; that is, you need to make measurements, changing only one variable at a time. Conducting controlled experiments is a basic principle of scientific investigation.
In the original experimental lab , you will use a Photogate to measure the period of one complete swing of a pendulum. By conducting a series of controlled experiments with the pendulum, you can determine how each of these quantities affects the period.
Figure 1
objectives
Measure the period of a pendulum as a function of amplitude.
Measure the period of a pendulum as a function of length.
Measure the period of a pendulum as a function of bob mass.
In our case, we will use the simulator,
https://phet.colorado.edu/sims/html/pendulum-lab/latest/pendulum-lab_en.html
click on the tab intro.
THeory
Using Newton’s laws, we could show that for small oscillations , the period, T , is related to the length, , and free-fall acceleration g by
, (1) or (2)
Procedure
1. Hang the 200 g mass. The length of the pendulum is the distance from the point on the rod halfway between the strings to the center of the mass. Start with a pendulum length of 70 cm.
2. Click on the ruler, stopwatch, and period trace.
Part I Amplitude
3. Move the mass out of the equilibrium position to the side about 10º from vertical and hold it. Click then release the mass. Write the time after five oscillations around the equilibrium position on the data table 1. Do the same for 15, 20,25,30 degree, record the data in your data table 1. The period T will be the value obtained in the stopwatch divided by 5 (number of oscillations)
Part II. Mass
6. Use three different masses to determine if the period is affected by changing the mass. Measure the period of the pendulum constructed with each mass, keeping the length of 70 cm and the initial angle of separation of 10 degree. In this case you will repeat the experiment for masses 0.200 Kg, 0.300 Kg, and 0.500 Kg.
Part III. Length.
7. Investigate the effect of changing pendulum length on the period. Use the 200 g mass and a consistent amplitude of 10º for each trial. Vary the pendulum length in steps of 10 cm, from 20 cm to 100 cm (measure the pendulum length from the rod to the middle of the mass). Record the data in the data table .
Data Table
Part I Amplitude. M=0.200Kg. L=0.70 m
Amplitude
ϴ(°)
Period
T(s)
10
15
20
25
30
Part II Mass. , ϴ=10º. L=0.70 m
Mass
(g)
Period
(s)
0.200
0.300
0.500
Part III Length. M=0.200Kg, ϴ=10º
Experiment
Theory
L:Length
T:Period
T² Period squared
T² Period squared
% error
(m)
(s)
(s²)
(s²)
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
1.00
Analysis
1. Complete the data table 1. Plot a graph of the pendulum period, T, vs. amplitude in degrees. Does the period depend on amplitude? Explain.
2. Complete the data table 2. Plot the pendulum period vs. mass. Does the period appear to depend on mass? Do you have enough data to answer conclusively?
3. Complete the data table 3 . Calculate T² using the formula (2). Calculate the percent error for all trials. Show all formulas and calculations for the last two rows
4. Plot the graph T² vs. . Identify the slope of the graph. What are the units of the slope?
5. Knowing the slope from the last graph, using the equation (2) calculate the experimental value of g on the earth. Calculate the percent error for g.
Show your formulas, calculations. Write the goal and the conclusions of the lab.
The post Pendulum Periods Name: Date: A swinging pendulum keeps a very regular beat. appeared first on PapersSpot.
