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Idling stop systems are being increasingly adopted in conventional engine vehicles as well as hybrid electric vehicles to increase fuel efficiency. When the engine starts, body vibration occurs that is caused by the rigid body eigenvalues of the power plant during initial combustion. Engine restart vibration after an idling stop is caused by the input force from the transmission, and the reaction force from the drive shaft as well as the input force from the engine. This phenomenon occurs frequently when the engine is restarted from the idling stop, the vibration is increasingly annoying to passengers. Usually, the vehicle development process is carried out in accordance with the V process. The V process divides the vehicle development process into two stages. The first stage is called the vehicle design stage to determine the characteristic. The second stage is called the vehicle verification stage to verify the performance.