A wooden block of mass M sits on a flat metal table that can be made to oscillate horizontally in simple harmonic motion. The coefficient of static friction between the block and table is u. When the table oscillates, the horizontal position x of the block can be expressed as x (t) = A cos (awt) where A is the amplitude of the oscillation and ø is the angular frequency of the oscillation. For a given amplitude, what is the maximum angular frequency at which the table can oscillate without the block slipping? Express your answer in terms of M, µ, A, and the acceleration due to gravity g.
A wooden block of mass M sits on a flat metal table that can be made to oscillate horizontally in simple harmonic motion. The coefficient of static friction between the block and table is u. When the table oscillates, the horizontal position x of the block can be expressed as x (t) = A cos (awt) where A is the amplitude of the oscillation and ø is the angular frequency of the oscillation. For a given amplitude, what is the maximum angular frequency at which the table can oscillate without the block slipping? Express your answer in terms of M, µ, A, and the acceleration due to gravity g.
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A wooden block of mass ? sits on a flat metal table that can be made to oscillate horizontally in
?(?)=?cos(??)
where ? is the amplitude of the oscillation and ? is the angular frequency of the oscillation. For a given amplitude, what is the maximum angular frequency at which the table can oscillate without the block slipping? Express your answer in terms of ?, ?, ?, and the acceleration due to gravity ?.
Transcribed Image Text:A wooden block of mass M sits on a flat metal table that can be made to oscillate horizontally in simple harmonic motion.
The coefficient of static friction between the block and table is µ. When the table oscillates, the horizontal position x of the
block can be expressed as
x (t) = A cos (@t)
where A is the amplitude of the oscillation and w is the angular frequency of the oscillation. For a given amplitude, what is
the maximum angular frequency at which the table can oscillate without the block slipping? Express your answer in terms of
M, µ, A, and the acceleration due to gravity g.
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