A horizontal platform moves up and down simple harmonically, the total movement being 10 cm. What is the shortest period permissible if objects resting on the platform are to remain in contact with it throughout the motion ?

Explanation

The object resting on the platform will not move if its maximum acceleration is equal to g.
i.e., `aomega^2 = g` where a is the amplitude
`omega^2=g/a`
`T = 2pi sqrt(a/g)`
Total vertical displacement = 10 cm
Amplitude a = 5 cm = 0.05 m
`T= 2xx3.14xxsqrt((0.05)/(9.8))=0.45s`