fig effect of linear damping that we introduce dimensionless independent and dependent variablestn tc un uc where tc and uc are characteristic sizes of time and displacementrespectivelysuch that tn and un have their typicalpsize around unity in the present problemwe can choose uc and tc = this gives the following scaled (or dimensionlessproblem for the dimensionless quantity tn/ un un cv un tn tn un vdp mk the striking fact is that there is only one physical parameter in this problemthe dimensionless number solving this problem corresponds to solving the original problem (with dimensionswith the parameters and howeversolving the dimensionless problem is more generalif we have solution tni /we can find the physical solution of range of problems since td un =mi as long as is fixedwe can find for any kand from the above formulain this waya time consuming simulation can be done only oncebut still provide many solutions this demonstrates the power of working with scaled or dimensionless problems