Question

A horizontal platform with an object placed on it is executing simple harmonic motion in the vertical direction. The amplitude of oscillation is 3.92×10^-3 m. What must be the least period of these oscillations, so that the object is not detached from the platform?

(a) 0.1256s

(b) 0.1356s

(c) 0.1456s

(d) 0.1556s

I have been asked this question at a job interview.

The doubt is from Periodic Motion topic in section Oscillations of Engineering Physics I

Answer 1

The correct answer is (a) 0.1256s

Explanation: For an object to get detached from the platform,

amax ≤g or ω^2 A≤g

(2π/T)^2 A≤g

Tmin=2π√(A/g)=2π√((3.92×10^-3)/9.8)

Tmin=2π×2×10^-2=0.1256s.