Damped simple harmonic motion experiment and questions?

1. The problem statement, all variables and given/known data

Hi, so my question is about a damped simple harmonic motion experiment

The experiment is as follows:

A 30 cm ruler with a needle attached to it is clamped to a bulldog clamp. The needle is placed in a beaker of water so that it is just inside the water ( by about 2cm) and the ruler is displaced so that its starting amplitude is 3.0cm. The ruler is then left to oscillate. The amplitude ( in cm ) after a number ‘n’ of oscillations is measured. The values used for ‘n’ are 5,10,15,20,25 and 30. InA is then calculated. A graph of InA against time is drawn.

The questions are:

1. Determine the gradient of the graph

2. Determine the y intercept

3.Using the equation A=A0e^-λn and your values of the gradient and y intercept ,determine the value of λ and A0 ( which should equal the initial amplitude used in the investigation)

4.Justify the number of significant figures used

I don’t want to know the actual answers to the question, which I why I haven’t uploaded the results or graph for the experiment, I would rather learn the methods behind the questions 🙂

2. Relevant equations

A=A0e^-λn
y=mx+c

A0–> initial amplitude

3. The attempt at a solution

1. So the gradient is just Δy/Δx, which equals ΔlnA/Δn, I got a value of -0.0313, however I was unsure what number of decimal places/sig figures I should leave it to, the values in the table are to 1 decimal place, so should it be -0.03?

2. The y intercept. Ok so I was a bit confused here, is the y intercept just simply where it crosses the y axis, so that it is in the form InA= or do I need to calculate A, from InA?
Again same question about number of decimal places/sig figures

3. This question caused me so much difficulty, I honestly have no idea how to approach it. I’m confused as to whether e^-λn= the gradient?! But the gradient is negative, so I can’t take ln of both sides?! If I could find λ, then I’m fine with finding A0, its just a case of rearranging?

4. The number of significant figures used in the answer should equal the least number of significant figures used in the data. Since λ is calculated using the gradient, which is to 1 significant figure, then λ must also be to 1 significant figure

Thank you so much 🙂

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