what is the dimensional formula of amplitude?
Young's Modulus = stress / strain
Strain = extension / original length [L] / [L] so it is a simple dimensionless ratio.
The dimensions of Young's modulus are therefore the same as the dimensions of stress.
stress = force / area
From Newton's 2nd Law, we know that force has the dimensions of mass * acceleration. So,
[stress] = [mass] * [acceleration] / [area]
[stress] = [ M ] * [L].[T]^-2 .[L]^-2