A vibration sensor, used in testing a washing machine, consists of a cube of alu

Question

A vibration sensor, used in testing a washing machine, consists of a cube of aluminum 1.50 cm on edge mounted on one end of a strip of spring steel (like a hacksaw blade) that lies in a vertical plane. The strip's mass is small compared with that of the cube, but the strip's length is large compared with the size of the cube. The other end of that strip is clamped to the frame of the washing machine that is not operating. A horizontal force of 1.45 N applied to the cube is required to hold it 2.95 cm away from its equilibrium position. If it is released, what is its frequency of vibration?

Explanation / Answer

This problem is just like a spring and mass. First, find thespring constant. You are told a force of 1.43 N is required fordisplacement of 2.75 cm so k = F / ?x = 1.45 N / 0.0295 m = 49.15254237288136 N/m now find the mass of the aluminum cube. You know it has volumeof V = 1.5 * 1.5 * 1.5 = 3.375 ccand the density of aluminum is 2.70 g/cc so the massis m = density * volume = 2.70 * 3.375 = 9.1125 grams And now... f = ( k / m)1/2 / 2? = ( 49.15254237288136 / 0.0091125)1/2 / 2? = = 11.68843627364413 Hz

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