Question

1.) Show the dimensional analysis for the equation Fs=-k deltax 2.) Show the dimensional analysis for...

1.) Show the dimensional analysis for the equation Fs=-k deltax

2.) Show the dimensional analysis for the equation T=2 pi square root (k/m)

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Answer #1

1) spring stiffness is given by Force/displacement

dimension of force = MLT-2

dimension of displacement = L

dimension of stiffness ,k= MLT-2/L = MT-2

dimension of change in length (delta x)= L

therefore, dimension of stiffness*delta x = MT-2*L = MLT-2

This matches dimension of force

2)dimension of k = MT-2

dimension of mass = M

dimension of k/m = MT-2/M = T-2

dimension of sqrt(k/m) = sqrt(T-2)=T-1

diemsnion of 1/sqrt(k/m) = T

This matches dimension of time period

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