Simple Harmonic Motion, spring periods

[Navras]

Hi guys! I'd really like help with this as I'm stuck.

Homework Statement

Investigate the mathmatical relationship between period of a spring and mass.
Finding the spring constant (k) from measuring periods with a spring and different hanging masses.

Homework Equations

T = 2pi SQRT(m/k)

or rearranged

T^2 = ((4pi^2)/k) m

The Attempt at a Solution

Used Excel to plot T^2 vs. hanging mass. T^2 in seconds squared (y-axis) and hanging mass in kg (x-axis). Used Excel to find the best fit line.

Since I have plotted T^2 vs. m, does the slope equal (4pi^2)/k ?

I don't know where to go from here to get k though.



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I've attached the graph I did also

 

[cepheid]

Welcome to PF!

Since I have plotted T^2 vs. m, does the slope equal (4pi^2)/k ?

Yeah. The relationship is linear in m. All the stuff (the coefficient) that multiplies m is therefore the slope, just like in any other linear relationship.

I don't know where to go from here to get k though.

What do you mean? You have the slope, which is 4pi^2 /k, from the best fit line. Therefore, you have k.

 

[Navras]

What do you mean? You have the slope, which is 4pi^2 /k, from the best fit line. Therefore, you have k.

So, the slope is 1.5129, does that mean k is 1.5129 or

is it (4pi^2)/1.5129 = k?

thanks :)

 

[cepheid]

So, the slope is 1.5129, does that mean k is 1.5129 or

is it (4pi^2)/1.5129 = k?

thanks :)

I'm not telling you the answer to that, you should be able to arrive at it using the information you have (and it should be really clear) . Consider these two statements:

1. The slope is 4pi^2/k

2. The slope is 1.5129 (according to the Excel best fit curve).

What do you conclude?