Introduction | Expressing | Measurement | Calculations | Graphs | Non-linear relationships | Investigations

## Under construction

## Anatomy of a report

## Aim

Your aim is a statement of what you are investigating. It should clearly state the variables and the relationship you are investigating.

The aim of this investigation is to investigate the relationship between the frequency a mass-spring system oscillates, and the amount of mass on the spring.

ExampleExample

The aim of this investigation is to investigate the relationship between the frequency a mass-spring system oscillates, and the amount of mass on the spring.

## Hypothesis

In this section you are to make a prediction of what you expect your experiment will show. Your prediction will need to be justified using relevant physics.

The force that the spring exerts is not dependant on mass (F = kx), and therefore will be the same for all masses. Since force doesn't change, Newton's 2nd law (F = ma) tells us that if the mass of the weight increases, its acceleration must decrease.

The equation "a = ω^2 x" shows that a decrease in acceleration is accompanied by a decrease in frequency. Furthermore, this equation shows the relationship is a square-relationship. Since the relationship between acceleration and mass is linear, this means that the relationship between mass and frequency must be a square-relationship as well. In other words, the mass will be proportional to the frequency squared.

In summary, I predict that an increase in mass will result in a decrease in frequency. Specifically, the mass will be proportional to the frequency squared.

__Example__The force that the spring exerts is not dependant on mass (F = kx), and therefore will be the same for all masses. Since force doesn't change, Newton's 2nd law (F = ma) tells us that if the mass of the weight increases, its acceleration must decrease.

The equation "a = ω^2 x" shows that a decrease in acceleration is accompanied by a decrease in frequency. Furthermore, this equation shows the relationship is a square-relationship. Since the relationship between acceleration and mass is linear, this means that the relationship between mass and frequency must be a square-relationship as well. In other words, the mass will be proportional to the frequency squared.

In summary, I predict that an increase in mass will result in a decrease in frequency. Specifically, the mass will be proportional to the frequency squared.

## Method

This should contain a detailed explanation as to how you will carry out your experiment. It is a good idea to include a diagram of how your equipment is set up.

It should also state what the variables in your experiment are. Recall that:

- The

- The

- All other variable are

I will determine the values of each of the masses exactly using a digital scale.

Using a stopwatch I will record the time taken for the spring to oscillate 10 times and find the average.The initial push or pull given to the mass will temporarily affect the period. To avoid this, I will start the stop watch once the spring has completed several oscillations.

I will use the average periods to calculate the frequencies of oscillation via f=1/T.

Independent variable: Amount of mass

Dependant variable: Frequency of oscillation

Control variables: The spring, the stopwatch and operator

**It should be detailed enough for another person to be able to recreate your experiment by reading it.**It should also state what the variables in your experiment are. Recall that:

- The

*independent variable*is the one whose value you are forcing. You choose the values for this variable, and manually adjust your equipment to them.- The

*dependant variable*is what you are measuring. It's value depends on the value of the independent variable.- All other variable are

*controlled variables*. These are variables that you will need to keep the same. They are variables that might have unwanted affects on your data.__Example__**As shown in the diagram to the right**, I will suspend a range of masses (approximately 50g, 100g, 150g, 200g, 250g, 300g) on a spring from a retort stand. I will weigh the retort stand down with textbooks to ensure that it does not move, as this could affect my results.I will determine the values of each of the masses exactly using a digital scale.

Using a stopwatch I will record the time taken for the spring to oscillate 10 times and find the average.The initial push or pull given to the mass will temporarily affect the period. To avoid this, I will start the stop watch once the spring has completed several oscillations.

I will use the average periods to calculate the frequencies of oscillation via f=1/T.

Independent variable: Amount of mass

Dependant variable: Frequency of oscillation

Control variables: The spring, the stopwatch and operator

## Results

Your results should be recorded in a results table.

**- Each measurement you make must include an uncertainty.****- You must state the units for all values****- All your values and uncertainties must be rounded correctly**## Analysis

In this course, you will need to draw two graphs for your analysis.

The first will be of your raw data. It should reveal the nature of the relationship between your independent and dependant variables (i.e. squared, square root, or inverse).

The second will be of your transformed data, such that the graph is linear. This is the graph that you will use to determine a value for the gradient and its uncertainty.

The first will be of your raw data. It should reveal the nature of the relationship between your independent and dependant variables (i.e. squared, square root, or inverse).

The second will be of your transformed data, such that the graph is linear. This is the graph that you will use to determine a value for the gradient and its uncertainty.

## Conclusion

This is where you summarise the findings of your investigation, and discuss the validity of your findings. Be sure to state any important results, and wherever possible, compare with theory.

## Evaluation

The purpose of this section is to reflect on the effectiveness and success of your investigation. Possible improvements, specifically with the aim of reducing uncertainty, should be discussed.