A shaker table is a tool used in engineering tests to find out how a device responds to vibrations. It is simply a platform that is able to oscillate vertically or horizontally with adjustable amplitude and frequency. Suppose a device of mass, m, is placed on top of the shaker table but not secured to it (it is placed loose on the table). The table is now set oscillating vertically in simple harmonic motion with an amplitude of 1 cm.
a) What is the maximum acceleration of the table without the device leaving contact with it?
b) At what frequency of oscillation does the device first start to leave contact with the table? At what point in the table's motion does the device leave contact with the table at this frequency? What is the period and angular frequency of the table at this frequency?
c) At the frequency found in b) what is the maximum speed of the table? At what point in the table's motion does it move at this speed?
d) Now suppose the table is set to oscillate horizontally (no vertical oscillation) at a frequency of 10 Hz. It is found that when the oscillation amplitude is 0.500 mm the device begins to slip on the surface of the table. What is the coefficient of static friction between the shaker table surface and the device?