Simple Harmonic Motion Lab Data Analysis

[Need_Help!!!]

Here is the problem I am having:
Professor told me to find the spring constant using our slope of the graph.
Now the graph that I did on the excel went something like this: On the X-axis of the graph was the weight of the hanging mass in Newtons and on the Y-axis of the graph was the elongation in meters.
I got the slope by adding tread line to my graph.

last piece of instructions that he gave to figure out the Spring constant was the Hook's Law, which is nothing more than F = -KX, where K is the spring constant and the negative sign just means the force and elongation are in opposite directions.

Now, I am stuck as to what do I do with the slope that I got from the graph created on the excel. What does my slope represent? What did I just found out when I got that slope? So far I have not been able to find via search engines that how do I actually use this graph and the slope to figure out my slope constant.

I know I am slow in understanding this elementary physics, but I need help. Hence my user name "Need_Help!"

So, can anyone out there help me out.


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Also, Does anyone out there know what does slope of Graph of the square of the period ( square * square ) versus the hanging mass's slope gives me?

What is the procedure on how to determine ( from my above graph ( you know the one with the graph of the square of the period versus the hanging mass ) ) and record what portion of the mass of the spring is oscillating along with the hanging mass?

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What does the slope of graph of square of the period ( period * period ) versus the length of the pendulum ) give me?

Because professor told me that I have to find the acceleration due to gravity, g , from the slop of the graph of square of the period versus the length of the pendulum by using this formula :$$T$$ = $$2\pi$$$$\sqrt{\frac{L}{g}}$$

someone please help.

 

[Shooting Star]

If the graph of a st line is passing through the origin, then the slope is nothing but the value of y/x at every point. If the slope is m, then m=y/x for any point (x,y). Since, you have plotted weight in the x direction and extension in the y direction, then slope = X/F = mod(1/k).
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T=2*pi*sqrt(M/k). This is the eqn for time period in SHM. Can you answer your 2nd Q from this? We get T^2= constant*M. This looks like a st line if you plot M and T^2.

All of the spring participates in the oscillation, and if the mass of the hanging weights are much greater than the mass of the spring, the latter can be neglected.
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Figure it out from what I have written in the first para.

 

[ogb p]

I can understand the confusion and frustration you are experiencing while trying to analyze your Simple Harmonic Motion lab data. Let me try to help you understand the concepts and procedures involved in finding the spring constant and other important values from your data.

First, let's start with the graph you created on excel. As you mentioned, the X-axis of the graph represents the weight of the hanging mass in Newtons and the Y-axis represents the elongation in meters. The slope of this graph represents the relationship between the weight and elongation, or in other words, how much the spring stretches for a given weight. This slope is directly related to the spring constant, which is a measure of the stiffness of the spring. The higher the slope, the higher the spring constant, indicating a stiffer spring.

Now, let's move on to the Hook's Law and how it relates to your data. As you said, Hook's Law states that F = -KX, where F is the force applied on the spring, K is the spring constant, and X is the elongation. By rearranging this equation, we can see that the slope of your graph (K) can be calculated by dividing the force (weight) by the elongation. So, you can use the slope of your graph to calculate the spring constant.

Moving on to the second part of your question, the slope of the graph of the square of the period (period * period) versus the hanging mass represents the relationship between the period of oscillation (time taken for one complete cycle) and the weight of the hanging mass. This slope can be used to determine the portion of the mass of the spring that is oscillating along with the hanging mass. This is because the period of oscillation is affected by the mass of the spring and the hanging mass.

Similarly, the slope of the graph of the square of the period versus the length of the pendulum represents the relationship between the period and the length of the pendulum. This slope can be used to calculate the acceleration due to gravity, as mentioned by your professor.

In conclusion, the slope of your graphs can provide valuable information about the properties of the spring and its oscillation. By understanding the concepts of spring constant, Hook's Law, and period of oscillation, you can use the slope of your graphs to calculate important values and analyze your data accurately. I hope this helps in your understanding and analysis of your lab data. Keep exploring and