Which of the following ideal systems can execute simple harmonic motion for sufficiently small displacements?
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Question

Which of the following ideal systems can execute simple harmonic motion for sufficiently small displacements?

G1 Physics · Accepted Answer

Each system develops a restoring force proportional to small displacement. For a U-tube, pressure-head difference is proportional to the displacement. The same is true for a V-tube after projecting the displacement vertically. For a floating body with constant water-line area, the change in buoyant force is ρgAx. For a gas piston, a small change in volume produces a pressure change proportional to displacement. Therefore all four can execute SHM under ideal small-displacement assumptions.