If the engine mount is the root of the problem, then the vibration will be coming from under the hood of the car. The engine mount is specifically designed to isolate the vibrations of the engine and prevent them from hitting the frame of the car, which then results in vibrations throughout. The engine mount has a special device in it, made from vulcanized rubber, which is meant to absorb vibration. If you notice a crack or excess wear in the rubber, it will need to be replaced to prevent further vibration.
One of the most common reasons for vibration in the car comes from the tires. Sit in the immobile car with the engine running and roll down the windows. Listen to where the noise of the vibration is coming from. If it sounds like it is coming from downwards near the tires, you can assume that is the point of origin. Check the tires for bumps, flat spot or areas of excessive wear and any signs of something being lodged in the tire or near the axle, which is the most common cause of vibration in the tire. If there is a rock wedged in the treads of the tire, simply remove it with your hands or with a pair of pliers. If there are bumps in the tires and you notice heavy vibration when you are coasting at around 45 mph, you need to get the tires replaced, because they are worn down to dangerous levels.
One of the less common areas where vibrations might originate is in the brake rotor. To check this, drive slowly at around 30 mph and tap the breaks. If the vibration in the car intensifies when you tap the breaks, the rotors are the origin points. In the presence of intense heat caused by friction of breaking, the brake pads will wear down causing metal on metal scraping, which results in vibration. Replacing of the brake pads or the rotor will remedy the vibration.
The universal joint is on the drive shaft and can cause vibration in some cases. Look at the universal joint. If you see a rust-colored powder around the bearings, this indicates that the universal joint is failing and must be replaced. Universal joint failing can result in poor car handling as well as very intense vibration. However, the joint itself cannot be repaired, only replaced.