Front end shake at 45-52 mph

I have a 2000 Buick Lesabre with 89,000 miles . I have recently begun to have a shake in the front end when I am accelerating between 45-52 MPH. It doesn’t shake if I am coasting at this speed only when excelerating. My mechanic tested out my tires they are not out of rond and my alignment is good. Can you help figure out what might be wrong and what I might be looking at in reapirs? I do not rememeber hitting any potholes but not being the only person who has driven my car lately I can only guess.

Wheel end related vibrations (those caused by tires and/or wheels) will be there regardless of acceleration or braking or coasting.

The shake is probably an indication that the engine or trans is not performing up to snuff.