1999 Toyota Corolla Car vibration

WHEN I START THE CAR IN THE MORNING IT GIVES A LIKE A WOBBLE AND CHANGING THE GEAR FROM REVERSE TO DRIVE IT ALSO GIVES A SLIGHT WOBBLE. I ALSO NOTICED WHEN THE CAR IS WARMED UP AND THE CAR IS STATIONARY ON DRIVE GEAR AND I TURN THE STEERING WHEEL LEFT OR RIGHT THE CAR VIBRATES, TURNING THE STEERING ACCELERATES THE CAR BUT BEFORE THE CAR ACCELERATES IT VIBRATES BEFORE THE RPM'S GOES UP. I WONDER IF IT IS THE ENGINE MOUNT IS BAD OR SOMETHING ELSE, THE CAR ALSO SHAKES OF VIBRATES WHEN THE CAR IS IDILING.

THANKS A LOT FOR YOUR HELP