Finding Spring Constant When Given Amplitude, Time, and Mass

In summary, the conversation discusses the process of using a line of best fit to solve a problem involving SHM equations. The equation T=(2(pi)((m/k)^1/2) is mentioned and the need to rewrite it in the form y=kx is emphasized. The conversation also includes a discussion about plotting a graph and finding the best straight line fit to the data points. Furthermore, the importance of rearranging the given equation and obtaining the correct variables for y and x is mentioned. Finally, the conversation ends with a clarification about the process of getting the equation into the specified form.
  • #1
physicsneedslabs
5
0
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.
 
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  • #2
physicsneedslabs said:
I averaged the masses and times
On what algebraic reasoning?
physicsneedslabs said:
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?
 
  • #3
haruspex said:
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.
 
  • #4
physicsneedslabs said:
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.
 
  • #5
haruspex said:
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.
C6D573AC-C4E8-44A8-B7D1-39689DE5D542.jpeg
35608C4C-7900-4303-8F2A-4B3FF247D3F3.jpeg

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.
 
  • #6
physicsneedslabs said:
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.
 
  • #7
haruspex said:
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)
 
  • #8
physicsneedslabs said:
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.
 
  • #9
haruspex said:
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.
 
  • #10
physicsneedslabs said:
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)
 

What is Hooke's Law and how does it relate to finding spring constant?

Hooke's Law states that the force exerted by a spring is directly proportional to the displacement of the spring from its equilibrium position. This means that the more a spring is stretched or compressed, the greater the force it exerts. This law is used to calculate the spring constant, which is a measure of the stiffness of a spring.

What are the units of spring constant?

The units of spring constant depend on the units used for amplitude, time, and mass. In the SI system, the units of spring constant are newtons per meter (N/m).

How do I calculate spring constant when given amplitude, time, and mass?

To calculate spring constant, you can use the formula k = (4π²m)/T², where k is the spring constant, m is the mass attached to the spring, and T is the period of oscillation (time for one complete cycle). You will need to convert the amplitude to meters and the time to seconds before plugging them into the formula.

Can I use a different formula to find spring constant?

Yes, there are other formulas that can be used to find spring constant. One alternative is k = (mg)/x, where m is the mass attached to the spring, g is the acceleration due to gravity, and x is the displacement from the equilibrium position. However, this formula is only applicable for vertical springs and may not be as accurate as the first formula mentioned.

What are some common sources of error when finding spring constant?

Some common sources of error when finding spring constant include inaccurate measurements of amplitude and time, variations in the mass of the object attached to the spring, and external factors such as air resistance or friction. It is important to take multiple measurements and calculate an average to minimize these errors.

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