Finding Spring Constant When Given Amplitude, Time, and Mass

[physicsneedslabs]

Homework Statement

Your lab instructor has asked you to measure a spring constant using a dynamic method-letting it oscillate-rather than a static method of stretching it. You and your lab partner suspend the spring from a hook, hang different masses on the lower end, and start them oscillating. One of you uses a meter stick to measure the amplitude, the other uses a stopwatch to time 10 oscillations. Your data are as follows:
[Mass(g)] {Amplitude(cm)} |Time(s)|
[100] {6.5} |7.8|
[150] {5.5} |9.8|
[200] {6.0} |10.9|
[250] {3.5} |12.4|

Use the best fit line of an appropriate graph to determine the spring constant.

Relevant Equations

T=(2(pi))((m/k)^(1/2)), Fnet=ma, Fg=mg, g=9.8m/s^2; Correct answer is 6.5N/m

I averaged the masses and times (which i took the time given and divided by 10 because in the problem it says you measure the time it takes to complete 10 oscillations) then plugged them directly into the T=(2(pi)((m/k)^1/2) and got the wrong answer. This is really confusing me because I don't really know how to start. And it was hard to format the chart so masses have [ ] around them, amplitudes have { } around them, and times have | | around them.

 

[haruspex]

I averaged the masses and times

On what algebraic reasoning?

it was hard to format the chart so masses have [ ] around them, amplitudes have { } around them, and times have | | around them.

Why would you want to?
You want a straight line. Precisely what should you plot against what to get a slope equal to k?

 

[physicsneedslabs]

On what algebraic reasoning?

in the problem it says to use the line of best fit, so i thought the process would include using the averaged values. I don't really know where to start here.

 

[haruspex]

in the problem it says to use the line of best fit, so i thought the process would include using the averaged values. I don't really know where to start here.

No, it means plot a graph that should, according to the equation, be approximately a straight line. Then find the best straight line fit to the data points.

First step is to rearrange the given equation into the form y=kx+c (but c will be zero), where y and x are some functions of T and m.

 

[physicsneedslabs]

No, it means plot a graph that should, according to the equation, be approximately a straight line. Then find the best straight line fit to the data points.

First step is to rearrange the given equation into the form y=kx+c (but c will be zero), where y and x are some functions of T and m.

I attached a photo of the problem and what I have done so far to help explain. I plotted an amplitude (given in the chart) vs. Force (calculated by mg of each mass because it is a vertical spring). I am not sure what to do next, I know the units of spring constant are N/m so I tried getting deltaF/deltaA but that still gave me the wrong answer.

The reason I put that equation in the given equations is because it is an important SHM equation that I am pretty sure is needed to solve this problem.

 

[haruspex]

The reason I put that equation in the given equations is because it is an important SHM equation that I am pretty sure is needed to solve this problem.

Indeed so. And you may notice amplitude does not appear in it.
As I advised, rewrite it in the form y=kx, where y and x are expressions using the other variables in the equation. Post what you get.

 

[physicsneedslabs]

Indeed so. And you may notice amplitude does not appear in it.
As I advised, rewrite it in the form y=kx, where y and x are expressions using the other variables in the equation. Post what you get.

solved for k: k=(m(4(pi^2)))/(T^2)

 

[haruspex]

solved for k: k=(m(4(pi^2)))/(T^2)

That's not in the form I specified. Get it as
(Some expression involving one of m, T)=k*(some expression involving the other of m, T)
In the graph, the expression on the left will give the y values, that on the right give the x values.

 

[physicsneedslabs]

That's not in the form I specified. Get it as
(Some expression involving one of m, T)=k*(some expression involving the other of m, T)
In the graph, the expression on the left will give the y values, that on the right give the x values.

Im confused as to which variable is supposed to be "y" and which is "y" supposed to be in terms of.

 

[haruspex]

Im confused as to which variable is supposed to be "y" and which is "y" supposed to be in terms of.

That's the second step. First step is to get it into the form I specified:
(Some expression involving one of m, T)=k*(some expression involving the other of m, T)