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?

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Answer 1 · 2018-01-18T10:36:01

$f =+-sqrt(2.56)$

$color(blue)("Determining the appropriate values")$
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: $color(white)("d")->k=2sqrt(2.56)$
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$color(blue)("Answering the question for "m=4)$

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

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

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