A mass stands on a platform that executes simple harmonic os

A mass stands on a platform that executes simple harmonic oscillation in a vertical direction

at a frequency of 5 Hz. Show that the mass loses contact with the platform when the

displacement exceeds 102 m.

f = 5 Hz

w = 2 pi f = 10pi rad/s

y = A sin(wt)

vy = dy/dt = A w sin(wt)

ay = d(vy) / dt = - A w^2 cos(wt)

when coming back at maximum position ( y = A)

cos(wt) = -1

ay = A w^2

if ay is greater than 9.8 m/s^2 then mass will lose contact.

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for this maximum amplitude (Amax)

9.8 = Amax ( 10 pi)^2

Amax = 0.01 m

if displacement exceeds more 0.01 m (or 10^-2 m), mass will lose contact with platform