Vibration damping device and elevator apparatus

A vibration damping device for reducing vibration of an elevator rope that is wound on and folded over one or more sheaves of an elevator, comprising:

• a displacement amplifier arranged around a region from a first portion of the elevator rope drawn from the one or more sheaves and a second portion of the elevator rope drawn from an opposite side of the one or more sheaves in parallel with the first portion, the displacement amplifier being configured to amplify a displacement of each of the first portion and the second portion of the elevator rope;
• and
• a limiting member that controls displacement amplification performed by the displacement amplifier such that the displacement of the first portion or the second portion amplified by the displacement amplifier does not become greater than a first displacement, the first displacement being a displacement of the elevator rope by which the elevator rope is not allowed to return to an equilibrium position of the vibration.