Algebra based physics exercise practice

[Julio Cesar]

1. "The problem statement" is more of a theory question based on physics. This would be my first post to this forum and I'm attempting to follow the rules as best I can. I guess the equation in question is T= 2∏√(m/k)



2. The above mentioned equation. According to my textbook author James S. Walker 4th Ed Physics text. This equation is called "Period of a Mass on a Spring"



3. My attempt at a solution is not a numerical answer because this is not a homework question. I don't know how to describe it but it involves looking at the equation and somehow knowing what will happen to one variable if another variable is changed. I honeslty would like some serious help with this as it seems that most of the other students in the course seem to have this down intuitively but I don't, I'm drowning. I hope this works to the moderators specifications. I don't know what else to write as this is a question from me and not a homework question.

Thanks

 

[CWatters]

T= 2∏√(m/k)

Ok. I would start but noting which parts are constants...

Obviously "2" and "∏" are constants.
"k" is the spring constant and depends on the physical properties of the spring. Normally they don't change unless you change the spring so we'll assume that's constant (I suppose some devious examiner might come up with a problem that involves changing the spring so watch out for that :-).

Then I'd rearrange all the constants so they are together...

T= 2∏√(m/k)

= √m * 2∏/√k

Then let's create a new constant A = 2∏/√k and the equation becomes..

T = A * √m

So fairly easy to see that the period T is proportional to the square root of the mass. Increase the mass and T increases. Since T=1/f the frequency reduces.

As an exercise work out what would happen if the mass was kept constant and the spring was heat treated somehow so the spring constant k reduced.