At a smooth horizontal table are two identical cubes of mass m , connected by a spring of rigidity k . The length of spring in the unstretched state is ℓ 0 . The right cube is linked to the load mas

Question

At a smooth horizontal table are two identical cubes of mass m , connected by a spring of rigidity k . The length of spring in the unstretched state is ℓ 0 ​ . The right cube is linked to the load mass m at the end. At some time the system is released and the system moves without initial velocity. Find the maximum distance (in cm) between blocks during the motion of the system.

TestHub · Accepted Answer

CM acceleration: a c m ​ = 3 m m g ​ = 3 g ​ . Equilibrium stretch: k x e q ​ = m ⋅ 3 g ​ ⇒ x e q ​ = 3 k m g ​ = 1 cm. Oscillation: ω 2 = μ k ​ = ( 2 m ) ( m ) k ( 2 m + m ) ​ = 2 m 3 k ​ = 500 rad 2 /s 2 . Released from rest with the spring unstretched, the extension oscillates between 0 and 2 x e q ​ = 2 cm. Maximum distance between the blocks = ℓ 0 ​ + 2 x e q ​ = 1 + 2 = 3 cm

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