engine shakes

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HI. I HAVE A 2000 CHEVY IMPALA. HAVE 110,000 MILES ON IT. MY PROBLEM IS THAT SOMETIMES WHEN I ACCELERATE LIKE BETWEEN 30-50 THE CAR SHAKES BUT LIKE AFTER 60 OR 70 GOES SMOOTH. KNOW I JUST NEW TIRES PUT ON, REPLACE THE BOLT JOINTS, REPLACE THE TIE RODS, AND HAVE A WHEEL BALANCE AND A WEEL ALIGMENT. AND STILL SHAKES, I DONT KNOW WHAT TO DO ENYMORE. PLEACE HELP ME ON THIS ONE.