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    Block M, with block m on top, executes SHM on frictionless surface. Find maximum amplitude for which m remains in place.

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    A block of mass M= 10 kg is on a frictionless horizontal surface. A small block whose mass is m= 1.0 kg is placed on the larger block. The coefficient of friction between the two blocks is u= .40. The two blocks execute SHM with a period T= 1.5 sec.
    Find Xm, the maximum amplitude possible, for which the small block does not slide on the surface of the larger block. See ATTACHMENT for diagram.

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    Solution Preview

    Physics required:
    A. The general equation giving location x(t) for an object executing SHM is:
    (1) x = Xm cos(w t + Qo) in which Xm is the amplitude, Qo is the initial phase angle in radians, and w is the angular frequency in rad/sec.
    B. In one period of time, T, the angle changes by '2 Pi' radians, therefore the angular frequency w, in terms of the ...