Oscillation in spring mass system questions

[xtrubambinoxpr]

Homework Statement

I am having an issue with answering number 4 in the attached image.

Homework Equations

Relevant equations are given in question 3.

The Attempt at a Solution

Squaring the equation would only make it easier to solve for any of the other variables, or the period squared. I cannot see the correlation with the square of the period. Would it just make it more accurate?

 

[jackarms]

It's an oddly worded question -- I think the only thing it's getting at is that, like you said, it would allow you to solve for m or k, and it would also allow you to see the relationships of the variables more clearly.

With the original equation you have:
$T = 2\pi\sqrt{\frac{m}{k}}$

So that means $T \propto \sqrt{\frac{1}{k}}$, so graphing $T$ vs. $\sqrt{\frac{1}{k}}$ would give you a linear relationship, and you could solve for k.

If you square both sides, you get:
$T^{2} = \frac{4\pi^{2}m}{k}$, so $T^{2} \propto \frac{1}{k}$, so graphing $T^{2}$ vs. $\frac{1}{k}$ would also give you a linear relationship, and you could solve for k that way too. So maybe that would be little easier? It really just depends on what data you have.

 

[xtrubambinoxpr]

It's an oddly worded question -- I think the only thing it's getting at is that, like you said, it would allow you to solve for m or k, and it would also allow you to see the relationships of the variables more clearly.

With the original equation you have:
$T = 2\pi\sqrt{\frac{m}{k}}$

So that means $T \propto \sqrt{\frac{1}{k}}$, so graphing $T$ vs. $\sqrt{\frac{1}{k}}$ would give you a linear relationship, and you could solve for k.

If you square both sides, you get:
$T^{2} = \frac{4\pi^{2}m}{k}$, so $T^{2} \propto \frac{1}{k}$, so graphing $T^{2}$ vs. $\frac{1}{k}$ would also give you a linear relationship, and you could solve for k that way too. So maybe that would be little easier? It really just depends on what data you have.

I see where you are coming from! just makes no sense to me to square it given I had all the variables in the experiment that we did in class. Maybe for future reference know this is something great to remember. Thanks Jack!