A potential function is given by U(x) = 18 x^2. What will be the acceleration (in meters/second ^2) of a 8.00 kg mass, when it is at the position x = 0.500 m?

Answer 1

That U(x) function results when the spring constant is 36. I am assuming that U is in joules.
At position x = 0.50, the force on the mass is 18 J.
Divide that by 8.0 kg for the acceleration.