A small wooden cube is placed on a plank. The plank performs a vertical S.H.M of frequency π 3 Hz . The maximum amplitude of the plank so that the wooden block does not leave the plank is [take g =

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A small wooden cube is placed on a plank. The plank performs a vertical S.H.M of frequency π 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 ]

TestHub · Accepted Answer

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: $ma \leq mg$ Therefore, $a \leq g$ . $∣ a ∣ = ω^{2} x$ when, $x = A$ the amplitude $∴ ω^{2} A \leq g or A \leq \frac{g}{ω ^{2}}$ Given, $f = \frac{3}{π} Hz \frac{ω}{2 π} = \frac{1}{T}$ $\Rightarrow ω = 6 Hz$ $A \leq \frac{10}{6 ^{2}} m$ $A \leq \frac{5}{18} m$

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