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Problem 1.37 - Problem 1.37[Difficulty 1 Given Equation for...

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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 quantity The first term of the equation is m d 2 x dt 2 The dimensions of this are M L t 2 × Each of the other terms must also have these dimensions. Hence c dx dt M L t 2 = so c L t × M L t 2 = and c M t = k x M L t 2 = so k L × M L t 2 = and k M t 2 = f M L t 2 = Suitable units for c, k, and f are c: kg s slug s k: kg s 2 slug s 2 f: kg m
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