A small wooden cube is placed on a plank. The plank performs a vertical S.H.M of frequency 3 Hz . The maximum amplitude of the plank so that the wooden block does not leave the plank is [take g=10 ~m / s ^2 ]

Step-by-step solution

Concept: wooden cube can leave the plank at the top extreme location when the plank just begins to move towards the equilibrium position. See the figure below: For cube not to leave plank the weight of the block should be more than the pseudo force on the cube: ma mg Therefore, a g . |a|= ^2 x when, x=A the amplitude ^2 ~A g or A g ^2 Given, f = 3 Hz 2 = 1 ~T =6 ~Hz A 10 6^2 ~m A 5 18 ~m