Vertical displacement of a plank with a body of mass m on it is y = sin(ωt) + √3 cos(ωt). The minimum value of ω for which the mass just breaks off the plank and the first time after t = 0 when this occurs are:
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Question

Vertical displacement of a plank with a body of mass m on it is y = sin(ωt) + √3 cos(ωt). The minimum value of ω for which the mass just breaks off the plank and the first time after t = 0 when this occurs are:

Options

G1 Physics · Accepted Answer

Combine y=sinωt+√3 cosωt=2 sin(ωt+π/3). The maximum downward acceleration is 2ω². For just losing contact, 2ω²=g, so ω=√(g/2). The first maximum positive displacement occurs when ωt+π/3=π/2, hence t=π/(6ω)=(π/6)√(2/g). Correct answer: A.