A table outfitted with springs on its feet bounces vertically in simple harmonic motion. A cup of

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A table outfitted with springs on its feet bounces vertically in simple harmonic motion. A cup of coffee is sitting on the table. Discuss whether any of the following changes to this system could cause the cup to lose contact with the table: 

\((a)\) increase the amplitude, 

\((b)\) increase the period,

(c) decrease the period, 

\((d)\) decrease the mass of the table, 

\((e)\) increase the mass of the table, 

\((f)\) change the phase of the motion. 

\((g)\) Would your answers be different if you considered not the cup bottom losing contact with the table but rather the coffee flying out of the cup?

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