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Question: in many industries a device that is often useful is...

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In many industries a device that is often useful is a “shaker table”. This is just a platform that oscillates (usually up and down, but some can oscillate in other directions as well). These are used for many things such as separating sand from gravel, and compacting materials. One common use for them is vibration testing. Often as a device is being developed it is useful to know how it responds to being vibrated (for example, devices that can’t survive fairly significant vibrations are not very useful in building cars...). Suppose that an electronics component is being vibration tested. The position vs. time data has been output from the shaker table and a computer has done a best fit to the data to determine the position as a function of time. The function is x(t) = (0.12 mm) cos[(1.57 × 102 s −1 )t] (a) What are the amplitude and period of this oscillation? (b) What are the maximum speed and maximum acceleration of the object on the shaker table? (c) Give two times when this object is going at its maximum speed. Explain how you know.

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