Question

The oscillation frequency f cycles per second, of a spring is inversely proportional to the square root of the mass m kg of the spring. When m=2.56, f=2, how do you find f when m=4?

Answer 1

`f =+-sqrt(2.56)`

Explanation:

`color(blue)("Determining the appropriate values")`
Inversely proportional `->a=k/b` where `k` is the constant of variation. So we have:

`f=1/(sqrt(m))xxk`

Initial condition:

`f=1/(sqrt(m))xxk color(white)("dddd") ->color(white)("dddd")2=1/sqrt(2.56)xxk`

So we have: `color(white)("d")->k=2sqrt(2.56)`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Answering the question for "m=4)`

`f=1/(sqrt(m))xxk color(white)("ddd")-> color(white)("ddd") f=1/sqrt(4)xx2sqrt(2.56)`

`color(white)("dddddddddddddd")-> color(white)("ddd")f=1/(+-2)xx2sqrt(2.56)`

`color(white)("dddddddddddddd")-> color(white)("ddd")f =+-sqrt(2.56)`