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This paper proposes an oil damper with a variable damping mechanism. The piston of the damper has a fan-shaped orifice as a flow channel for the oil. The magnitude of damping can be regulated continuously by varying the area of the orifice. Another merit of this damper is that its damping can be regulated as viscous, enabling a theoretical approach to be used in its study. We have analyzed the oil damper by assuming the flow of oil to be laminar and oscillatory. However, it is too difficult to obtain an analytical solution from the basic equation, so the analysis was accomplished numerically using the finite difference method. It was confirmed that the theoretical results agree well with the experimental ones.