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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 planeThe strip's mass is small compared with that of the cube, but the strip's length is large compared with the size of the cubeThe other end of that strip is clamped to the frame of the washing machine that is not operatingA horizontal force of 1.50 N applied to the cube is required to hold it 2.50 cm away from its equilibrium positionIf it is released, what is its frequency of vibration?I don't even know where to start! Help please! Thanks so much!

Answer:

The relevant equation is: dQ mcdT As dQ (change of thermal energy) and mass are the same, the equation can be rewritten as: cdTconstant So a material with a lower specific heat capacity will have a greater increase in temperatureThe question has already stated this but now we know they are inversely proportionalThus: c of aluminium/c of copper dT of aluminium / dT of copper 0.22/0.092 proportionality constant 2.39 So copper will be 2.4 times hotter than aluminium (or aluminium will be 0.42 times hotter than copper).
The copper takes more energy (heat) to raise it the same temperature as the aluminumSo with equal amounts of energy, the copper doesn't warm up as much 0.092 / 0.22 0.42 .
Find the mass m of the aluminum cubex 0.025, F 1.5 accel F/m omega^2 accel/x Or you can mentally replace the leaf spring with an equivalent conventional spring attached transversely to the cubek F/x omega^2 k/m

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