Simple pendulum
Goals
The purpose of the lab experiment is to explore simple harmonic motion (SHM). We will accomplish this through the validation of harmonic calculations and ultimately creating a time piece (oscillator)
Method
In part A (Simple Pendulum) we will measure the effects of mass on the period of the pendulum. We will also calculate the period using small angular displacements and compare the results. We will also explore the effects on the period when the angular displacement is not “very small” (in essence > 10°). Lastly we will look at creating our own pendulum clock to create a period of 1 second.
In part B (Mass on a Spring) we will experiment with oscillations of a spring. We will then estimate the spring constant. Based on the spring constant we will then calculate the mass need to create a period of 1 second with our spring.
In Part C (Physical Pendulum) we will determine gravity within the classroom.
Figure 1: Pendulum with photogate
Figure 2: Hanging mass on Spring
Figure 3: Physical Pendulum
Data and Results
Part A: Simple Pendulum
First we set up a pendulum with a hanging mass suspended from it. The pendulum moving through a small angular displacement passes through a photogate which is recorded and then averaged below
m = 100 g = 0.1 kg
Pendulum Width = .022 m
Θ < 10° (Small angular displacement)
L = 0.71 m
Table 1: Measured period (T)
Run
Period (T)
1
1.6892 s
2
1.6904 s
3
1.6911 s
4
1.6837 s
5
1.6844 s
Measured (average) period (T) through the photogate = Tavg = 1.69 s
Next we calculated the expected period using the length of the string with uncertainty accounted for.
Calculated period (T):
Formula: T = 2π*sqrt(L/g)
Calculation:
T = 2π*sqrt( 0.71m / 9.8 m/s2) = 1.69 s
Next we explored the effects of changing the mass suspended from the string.
m = 200 g
L = 0.72 m
Table 2: Mass’ effect on the period
Mass
Average Period (T)
0.1 kg
1.69 s
0.2 kg
1.69 s
0.25
The purpose of the lab experiment is to explore simple harmonic motion (SHM). We will accomplish this through the validation of harmonic calculations and ultimately creating a time piece (oscillator)
Method
In part A (Simple Pendulum) we will measure the effects of mass on the period of the pendulum. We will also calculate the period using small angular displacements and compare the results. We will also explore the effects on the period when the angular displacement is not “very small” (in essence > 10°). Lastly we will look at creating our own pendulum clock to create a period of 1 second.
In part B (Mass on a Spring) we will experiment with oscillations of a spring. We will then estimate the spring constant. Based on the spring constant we will then calculate the mass need to create a period of 1 second with our spring.
In Part C (Physical Pendulum) we will determine gravity within the classroom.
Figure 1: Pendulum with photogate
Figure 2: Hanging mass on Spring
Figure 3: Physical Pendulum
Data and Results
Part A: Simple Pendulum
First we set up a pendulum with a hanging mass suspended from it. The pendulum moving through a small angular displacement passes through a photogate which is recorded and then averaged below
m = 100 g = 0.1 kg
Pendulum Width = .022 m
Θ < 10° (Small angular displacement)
L = 0.71 m
Table 1: Measured period (T)
Run
Period (T)
1
1.6892 s
2
1.6904 s
3
1.6911 s
4
1.6837 s
5
1.6844 s
Measured (average) period (T) through the photogate = Tavg = 1.69 s
Next we calculated the expected period using the length of the string with uncertainty accounted for.
Calculated period (T):
Formula: T = 2π*sqrt(L/g)
Calculation:
T = 2π*sqrt( 0.71m / 9.8 m/s2) = 1.69 s
Next we explored the effects of changing the mass suspended from the string.
m = 200 g
L = 0.72 m
Table 2: Mass’ effect on the period
Mass
Average Period (T)
0.1 kg
1.69 s
0.2 kg
1.69 s
0.25