Problem 1.37[Difficulty: 1]Given:Equation for vibrations.Find:Dimensions of c, k and f for a dimensionally consistent equation. Also, suitable units in SI and BG systems.Solution:Use the vibration equation to find the diemsions of each quantityThe first term of the equation ismd2xdt2⋅The dimensions of this areMLt2×Each of the other terms must also have these dimensions.Hencecdxdt⋅ML⋅t2=socLt×⋅t2=andcMt=kx⋅⋅t2=sokL×⋅t2=andkMt2=f⋅t2=Suitable units for c, k, and f arec:kgsslugsk:kgs2slugs2f:kg m⋅s2slug ft
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