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SHM vertically moving tray with loose cube on top. Given period, find amplitude max., and given amplitude, find minimum period.

A tray is moving with SHM along a vertical y axis. A small aluminum cube is placed on the tray.
a. If the period is fixed at T= 1.5 sec, find the maximum amplitude Ym for which the cube remains in contact with the tray.
b. If the amplitude is fixed at Ym= .15 m, find the minimum period T for which the cube remains in contact with the tray.

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Physics statements:
A. The acceleration of a point moving with SHM is always toward the center.
B. The acceleration is zero at the center and maximum at end points.
C. The maximum possible downward acceleration of the unattached cube is 'g'.
D. The general equation giving y(t) for SHM motion on a y axis, with y=0 at origin, in
which w is the angular frequency in rad/sec and Q is the initial phase, ...

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