Investigation of the Factors Affecting the Period of Vibration of a Weighted Cantilever
Investigation of the factors affecting the period of vibration of a weighted cantilever
Introduction
The aim of the experiment is to find out how the period T of vibration of a weighted cantilever depends on the vibrating length L.
Hypothesis:
Assume the relationship between the vibrating period T and vibrating length L is in accord with the equation: T=kLn, where k and n are both constant values.
According to the hypothesis, the vibrating period T and vibrating length L is a linear relationship, so we take logarithms on both sides of the equation. Then, we can get a new equation, which is shown as the following:
logT=logk＋nlogL
Variables:
In this experiment, the independent variable is L, the length of vibration. The dependent variable is T, the time taken to complete the oscillation. The controlled Variables is the the amplitude of the oscillation.
Materials required:
1 G-clamps
1 set of standard masses steel ruler(the cantilever) stop watch
Methods
Before the experiment, set-up the standard mass at the top of the steel ruler(the cantilever).
Step 1: using the G-clamps to set the certain length of vibration.
Step 2: pressing the standard mass at the top of the steel ruler and then release it.
Step 3: as soon as we release the standard mass, using the stop watch to record the time taken for 10 periods.
Step 4: changing the length of the steel ruler and repeat doing the steps above.
Data collection
In this experiment, I choose 30cm, 35cm, 40cm, 45cm, 50cm, and 55cm as the different lengths of the steel ruler. The time taken for completing 10 periods of vibration at each length is shown in the following table.
Table 1- row data
| length(L/m) |time taken(t/s) |
| 0.30 |2.1 |1.9 |2.0 |2.0 |2.0 |
| 0.35 |2.5 |2.6
Introduction
The aim of the experiment is to find out how the period T of vibration of a weighted cantilever depends on the vibrating length L.
Hypothesis:
Assume the relationship between the vibrating period T and vibrating length L is in accord with the equation: T=kLn, where k and n are both constant values.
According to the hypothesis, the vibrating period T and vibrating length L is a linear relationship, so we take logarithms on both sides of the equation. Then, we can get a new equation, which is shown as the following:
logT=logk＋nlogL
Variables:
In this experiment, the independent variable is L, the length of vibration. The dependent variable is T, the time taken to complete the oscillation. The controlled Variables is the the amplitude of the oscillation.
Materials required:
1 G-clamps
1 set of standard masses steel ruler(the cantilever) stop watch
Methods
Before the experiment, set-up the standard mass at the top of the steel ruler(the cantilever).
Step 1: using the G-clamps to set the certain length of vibration.
Step 2: pressing the standard mass at the top of the steel ruler and then release it.
Step 3: as soon as we release the standard mass, using the stop watch to record the time taken for 10 periods.
Step 4: changing the length of the steel ruler and repeat doing the steps above.
Data collection
In this experiment, I choose 30cm, 35cm, 40cm, 45cm, 50cm, and 55cm as the different lengths of the steel ruler. The time taken for completing 10 periods of vibration at each length is shown in the following table.
Table 1- row data
| length(L/m) |time taken(t/s) |
| 0.30 |2.1 |1.9 |2.0 |2.0 |2.0 |
| 0.35 |2.5 |2.6