A block of mass m is placed on a smooth horizontal surface and connected between two ideal springs fixed to opposite walls. The left spring has force constant k and the right spring has force constant 2k. If the block is displaced slightly and released, what is its angular frequency?
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Question

A block of mass m is placed on a smooth horizontal surface and connected between two ideal springs fixed to opposite walls. The left spring has force constant k and the right spring has force constant 2k. If the block is displaced slightly and released, what is its angular frequency?

Options

G1 Physics · Accepted Answer

If the block is displaced by x to one side, both springs provide restoring forces towards equilibrium. Total restoring force: F = −kx−2kx = −3kx. Thus, kₑ = 3k. Therefore, ω = √[kₑ/m] = √(3k/m). Correct option: C.