Simple Harmonic Motion, spring periods (2024)

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

Welcome to PF!

Navras said:

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.

Navras said:

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.

cepheid said:

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 :)

Navras said:

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?

Hello,

It looks like you're on the right track in investigating the relationship between the period of a spring and mass. As you have correctly stated, the equation for the period of a spring is T = 2pi SQRT(m/k), where T is the period, m is the mass, and k is the spring constant.

By rearranging the equation, we can see that T^2 is directly proportional to m. This means that as the mass increases, the period of the spring will also increase. This is because a heavier mass requires more force to stretch the spring, resulting in a longer period.

In order to find the spring constant k, you can use your plotted data and the slope of the best fit line. The slope of the line should be equal to (4pi^2)/k. So, if you calculate the slope of your line, you can use it to solve for k.

I hope this helps. Keep up the good work in investigating the relationship between period and mass in simple harmonic motion!