Question

A horizontal platform vibrate up and down with a simple harmonic motion of amplitude 20 cm. At what frequency will an object kept on the platform just lose contact with the platform? [Take g = 9.81 m/s²]

Answer 1

Let m be the mass of the object and A be the amplitude of motion of platform. If R₁ is the normal reaction of the platform at the highest point then

(mg - R₁) = mω²A

R₁ = (mg – mω²A)  .. (1)

At the lowest point, if R₂ is the normal reaction of the platform, then

When the object is about to leave the platform the normal reaction of the surface is zero. From (1) and (2), it can be seen that the object can leave the platform only at the highest point.