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-2T-2, and the Amplitude A, with dimensions L. Use dimensional analysis to show what the period of oscillation would be proportional to.
The Attempt at a Solution
So we know that P∝ makbAc(a,b and c are numerical exponents to be determined). So rewriting P(period of oscillation) into its dimensions, we get MxML-2T-2L which then simplifies to M2L-1T-2. That is equal to Ma(M/L2T2)bLc. 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∝m2AK. The problem is this is not a possible solution since its a multiple choice question.