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## Homework Statement

The period of oscillation of a nonlinear oscillator depends on the mass m, with dimensions M; a restoring force constant k with dimensions of ML

^{-2}T

^{-2}, and the Amplitude

*A*, with dimensions L. Use dimensional analysis to show what the period of oscillation would be proportional to.

## Homework Equations

N/A

## The Attempt at a Solution

So we know that P∝

*m*

^{a}k

^{b}A

^{c}(a,b and c are numerical exponents to be determined). So rewriting P(period of oscillation) into its dimensions, we get MxML

^{-2}T

^{-2}L which then simplifies to M

^{2}L

^{-1}T

^{-2}. That is equal to M

^{a}(M/L

^{2}T

^{2})

^{b}L

^{c}. Then multiplying our unknown exponents into our dimensions and setting them equal to the dimension exponents on the right, we should get: a+b=2, -2b+c=-1, -2b=-2. Solving for each variable we get: b=1, a=2, c=1. Then redefining our dimensions into their respective units I got: P∝m

^{2}AK. The problem is this is not a possible solution since its a multiple choice question.

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