0
$\begingroup$

I am confused as to how to go about the following question.

The question explains that f refers to the frequency of an oscillation, $m$ refers to the mass of an object attached to a spring, $k$ refers to the spring constant, and $c$ refers to some dimensionless constant.

And I am asked this:

By writing $f$ = $c m^x k^y$ and matching units on both sides, show that $f = c \cdot \sqrt{k/m}$.

Would this problem be solved if I simply used the law of exponents and rewrote the expression for $f$ as $f = c \cdot k^{1/2} \cdot m^{-1/2}$ ?

I would like to ask for your advice in understanding what the point of this question is and how to "show" what it is asking for.

In addition, it would be of great help if you could expound on what "matching units on both sides" refer to. Is it referring to dimensional analysis?

$\endgroup$
0
$\begingroup$

I guess the question is: Suppose there exist an $x$ and a $y$ such that $f=c*m^x*k^y$. Then, by using unit based considerations, find $x$ and $y$. You basically did that. Perhaps you also need to show that there are no other possible solutions.

The question shows that unit based analysis (units being kg, sec, etc.. and must be identical on both sides of the equation) may sometimes provide quick solutions.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.