A child of mass m sits on top of a rectangular slab of mass M = 35 kg , which in turn rests on the frictionless horizontal floor at a pizza shop. The slab is attached to a horizontal spring with spring constant k = 450 N/m (the other end is attached to an immovable wall, the figure (Figure 1). The coefficient of static friction between the child and the top of the slab is μ = 0.40. The shop owner's intention is that, when displaced from the equilibrium position and released, the slab and child (with no slippage between the two) execute SHM with amplitude A = 0.54 m .
What is this minimum value of mass of the child?

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02-12-2022
Physics

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A child of mass m sits on top of a rectangular slab of mass M = 35 kg , which in turn rests on the frictionless horizontal floor at a pizza shop. The slab is attached to a horizontal spring with spring constant k = 450 N/m (the other end is attached to an immovable wall, the figure (Figure 1). The coefficient of static friction between the child and the top of the slab is μ = 0.40. The shop owner's intention is that, when displaced from the equilibrium position and released, the slab and child (with no slippage between the two) execute SHM with amplitude A = 0.54 m .
What is this minimum value of mass of the child?

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