Investigation of pendulum & gravity
Research question: How does the time period depend upon the strength of gravitational field
(How does the strength of the gravitational field affect the time period of the pendulum?
Introduction
For this experiment, I will be focusing on pendulums and gravitational force. For the setup, it
would be a simple pendulum, which is a bob/mass that is suspended to a string that lets it
swing back and forth. Pendulums have always been something really mesmerizing to me,
even when I did not realise it, as a child, I thought it would be really fun and exciting to
become the bob in a pendulum, to be swinging in speed, feeling the breeze on my face, which
now that I think about it, is why the swing set was my favorite equipment of the whole
playground, because I technically become part of a pendulum, I remember going back and
forth really fast by extending my legs while I go forwards, and closing it as I go back.
Everytime I see a swing set or a swinging chair, I feel the urge to get on it. Unsurprisingly,
my favorite superhero as a child was Spider-man. I would rewatch the movies and replayed
the games again and again mainly because of how satisfying it was to watch him swing
around buildings with his unrealistic durable webbing. For the setup, I would not tire myself
by making an actual pendulum and since it is impossible for me to change the strength of the
gravitational field, I will be using a computer simulation which gives me control of almost all
the conditions/variables.
Short background information source
Pendulum
A pendulum is a device which consists of a mass which is suspended from a fixed point, and
it can swing back and forth due to the gravitational field. When a kid gets on a swing,
basically they become the bob/mass which is swinging back and forth.
Time period
The time period of a pendulum, is the time it takes for the bob to complete an oscillation, the
time period in pendulums are constant, but it can be affected by the length of string and the
gravitational field, but the mass of bob has no effects on the time period, due to F=ma, the
mass is directly proportional to the force but changing m, mass will have no effect on the
acceleration, hence it will stay the same.
Formula for time period of pendulum
L
T = 2π √ /g
T= time period(seconds)
L= length of string(m)
g= gravitational acceleration(m/s^2)
Another method to find out the time period per oscillation, is to observe and count manually a
certain amount of oscillations(let’s say 10) made while keeping track of the time, then right
after 10 oscillations, stop the stopwatch and record the time. Let's say the time is 14 seconds,
14 seconds to complete 10 oscillations. Do simple maths 14/10 = 1.4 so it takes 1.4 seconds
per oscillation, which makes the time period, T 1.4 seconds.
Research question: “How does the strength of the gravitational field affect the time
period of the pendulum?”
Hypothesis
I predict that increasing the gravitational acceleration will increase the speed of the
pendulum, which causes the time period to be faster, shorter. I think that this would be the
result because, the stronger the gravity, the faster the mass would be pulled downwards since
clearly there is more force on it. If the gravitational force is weak, then objects tend to be
lighter and “floaty” even, so they have more time in the air, making the oscillations longer.
Using the main formula that is T= 2π √L/g , we can just say the controlled length is 0.5m.
Now if the gravitational acceleration is 10m/s, then it would be 2π √0.5/10 = 1.40 seconds
But if it was on another planet with gravitational acceleration of 15m/s then it would be
2π √0.5/15 = 1.15 seconds, which is shorter/faster than on Earth.
Design
Variable type
what
Unit
How to
measure/vary/contr
ol
Why
Independent
Gravitational
acceleration
M/s^2
Using the slider
which controls the
gravity in the
simulation
To test if changes in
gravity can cause changes
in the time period
Dependent
Time period(time
for one
oscillation
seconds(s)
Stopwatch provided
in simulation to
time how long it
takes for 5
oscillations then
divide it by 5.
To know the different time
periods and compare
them.
Controlled
Length of string
Meters(m)
Just do not change
the length settings
keeping it at 0.7m
which is default.
Different length of string
can affect the time period
Controlled
Mass of bob
Kg
Just by not
changing the
settings of mass,
keep it at 0.8 kg
Different mass actually
does not affect the time
period, but should keep it
the same to make it fair
controlled
The angle at
which the
pendulum is
dropped
degrees(°)
There is already
protractor where the
fixed point is, I will
drop it from the
same angle every
trial 50°
Different type of strings
have different
stretchability which
affects the tension
Setup
Pendulum Simulation from PHET
Note: The gravity changer in the simulation does not have numbers on them, so I used a
different tool called “screen ruler” which measures px(pixels). The gravity for earth
(10m/s^2) is at 5 px, which means that every 5.3 px is 1m/s^2. Another setting is Jupiter,
which has the gravitational acceleration of 25m/s^2. To test if the gravity slider is
accurate, 25x5.3=132.5
The reading was 132-133 px, so it was actually pretty accurate.
1 m/s^2 = 5.3px
The simulator has a “slow mode” which makes things move in slow motion, and it also
makes the stopwatch slower, so this would be useful for more accurate results
Materials needed
- computer simulation
- stopwatch
Method
1.
2.
3.
4.
5.
6.
7.
8.
Open the simulator
Set the length of string to 0.70 m
Set the mass to 0.80 kg
Prepare the stopwatch
Set the gravitational acceleration to 5 m/s^2
Pull the pendulum back on the angle of 50° then drop it
Wait for it to swing back and forth once then start the stopwatch
Count 5 full oscillations(before the last oscillation use the “slow mode ” feature to be
more accurate )
9. Stop the stopwatch right after the fifth oscillation
10. Record the time
11. Repeat the experiment two more times
12. Repeat 5-11 for different gravitational accelerations.
13. Find out the average time for each gravitational acceleration and get Time period
Safety precautions
- Don’t put your eyes very close to the screen to observe the pendulum moving, it will
give you eye strains, observing it from far will be enough.
Data collection
Controlled variables
Mass of bob (kg)
Length of string (m)
Angle relative
0.80
0.70
50°
Gravitational
acceleration
(m/s^2)
Time taken for 5 complete
oscillations (s)
Time average
avg (s)
Time period(s)
Trial 1
Trial 2
Trial 3
5.00
13.1
13
13
13.03
2.61
10.0
8.70
8.70
8.70
8.70
1.74
15.0
7.10
7.00
7.20
7.10
1.42
20.0
6.20
6.30
6.30
6.27
1.25
25.0
5.50
5.50
5.40
5.47
1.10
Processed data graph
In this graph, there is a clear downtrend, as the value of gravitational acceleration increases,
the time period seems to decrease. The decrease is -0.87, -0.32, -0.17, -0.15. We can see
from here that the amount of decrease the time period gets, is decreasing itself. This is also
noticeable in the graph, the line which connects the dots does not form a straight line going
down, instead looks more like a curve.
Conclusion
Initially I predicted for there to be a negative correlation with the two variables, “increase in
gravitational acceleration would make the time faster, decreasing it” and from the results of
the experiment, it actually strongly supports my hypothesis, because when I increased the
gravitational acceleration, it shows a faster time period than the previous gravitational
acceleration, which is smaller.
But initially I expected a more linear and straight line from the graph, but I believe this is still
quite accurate because the formula is T= 2π √L/g.
Evaluation
In this experiment, I believe that things went well and there are actually very little to no
errors, and that is mainly because of how I carried out the experiment, that is using a
computer simulation, it is pretty accurate and my human error does not interfere with the
whole experiment. If I were to do this in real life, I might have problems trying to drop it
from the same height and angle, while the simulation had a built-in protractor that displays
the value.
For the timing(starting and stopping stopwatch), there were not many difficulties, because of
the feature that allows the pendulum to go in slow motion. During the 3 trials of each
different gravitational acceleration, they were all the same number and the largest difference
among them is just 0.2, or 200 milliseconds, which does not affect the experiment and it is
still reliable. For the accuracy I think it was really accurate because I was using a computer
program.